# Dragon curve

Dragon curve
You are encouraged to solve this task according to the task description, using any language you may know.

Create and display a dragon curve fractal.

(You may either display the curve directly or write it to an image file.)

Algorithms

Here are some brief notes the algorithms used and how they might suit various languages.

• Recursively a right curling dragon is a right dragon followed by a left dragon, at 90-degree angle. And a left dragon is a left followed by a right.
*---R----*     expands to     *       *
\     /
R   L
\ /
*

*
/ \
L   R
/     \
*---L---*      expands to     *       *
The co-routines dcl and dcr in various examples do this recursively to a desired expansion level.
• The curl direction right or left can be a parameter instead of two separate routines.
• Recursively, a curl direction can be eliminated by noting the dragon consists of two copies of itself drawn towards a central point at 45-degrees.
*------->*   becomes    *       *     Recursive copies drawn
\     /      from the ends towards
\   /       the centre.
v v
*
This can be seen in the SVG example. This is best suited to off-line drawing since the reversal in the second half means the drawing jumps backward and forward (in binary reflected Gray code order) which is not very good for a plotter or for drawing progressively on screen.
• Successive approximation repeatedly re-writes each straight line as two new segments at a right angle,
                       *
*-----*   becomes     / \      bend to left
/   \     if N odd
*     *

*     *
*-----*   becomes    \   /     bend to right
\ /      if N even
*
Numbering from the start of the curve built so far, if the segment is at an odd position then the bend introduced is on the right side. If the segment is an even position then on the left. The process is then repeated on the new doubled list of segments. This constructs a full set of line segments before any drawing.
The effect of the splitting is a kind of bottom-up version of the recursions. See the Asymptote example for code doing this.
• Iteratively the curve always turns 90-degrees left or right at each point. The direction of the turn is given by the bit above the lowest 1-bit of n. Some bit-twiddling can extract that efficiently.
n = 1010110000
^
bit above lowest 1-bit, turn left or right as 0 or 1

LowMask = n BITXOR (n-1)   # eg. giving 0000011111
BitAboveLowestOne = n BITAND AboveMask
The first turn is at n=1, so reckon the curve starting at the origin as n=0 then a straight line segment to position n=1 and turn there.
If you prefer to reckon the first turn as n=0 then take the bit above the lowest 0-bit instead. This works because "...10000" minus 1 is "...01111" so the lowest 0 in n-1 is where the lowest 1 in n is.
Going by turns suits turtle graphics such as Logo or a plotter drawing with a pen and current direction.
• If a language doesn't maintain a "current direction" for drawing then you can always keep that separately and apply turns by bit-above-lowest-1.
• Absolute direction to move at point n can be calculated by the number of bit-transitions in n.
n = 11 00 1111 0 1
^  ^    ^ ^     4 places where change bit value
so direction=4*90degrees=East
This can be calculated by counting the number of 1 bits in "n XOR (n RIGHTSHIFT 1)" since such a shift and xor leaves a single 1 bit at each position where two adjacent bits differ.
• Absolute X,Y coordinates of a point n can be calculated in complex numbers by some powers (i+1)^k and add/subtract/rotate. This is done in the gnuplot code. This might suit things similar to Gnuplot which want to calculate each point independently.
• Predicate test for whether a given X,Y point or segment is on the curve can be done. This might suit line-by-line output rather than building an entire image before printing. See M4 for an example of this.
A predicate works by dividing out complex number i+1 until reaching the origin, so it takes roughly a bit at a time from X and Y is thus quite efficient. Why it works is slightly subtle but the calculation is not difficult. (Check segment by applying an offset to move X,Y to an "even" position before dividing i+1. Check vertex by whether the segment either East or West is on the curve.)
The number of steps in the predicate corresponds to doublings of the curve, so stopping the check at say 8 steps can limit the curve drawn to 2^8=256 points. The offsets arising in the predicate are bits of n the segment number, so can note those bits to calculate n and limit to an arbitrary desired length or sub-section.
• As a Lindenmayer system of expansions. The simplest is two symbols F and S both straight lines, as used by the PGF code.
Axiom F, angle 90 degrees
F -> F+S
S -> F-S

This always has F at even positions and S at odd. Eg. after 3 levels F_S_F_S_F_S_F_S. The +/- turns in between bend to the left or right the same as the "successive approximation" method above. Read more at for instance Joel Castellanos' L-system page.

Variations are possible if you have only a single symbol for line draw, for example the Icon and Unicon and Xfractint code. The angles can also be broken into 45-degree parts to keep the expansion in a single direction rather than the endpoint rotating around.

The string rewrites can be done recursively without building the whole string, just follow its instructions at the target level. See for example C by IFS Drawing code. The effect is the same as "recursive with parameter" above but can draw other curves defined by L-systems.

## ALGOL 68

Translation of: python
Works with: ALGOL 68G version Any - tested with release algol68g-2.8.
File: prelude/turtle_draw.a68
# -*- coding: utf-8 -*- # STRUCT (REAL x, y, heading, BOOL pen down) turtle; PROC turtle init = VOID: (  draw erase (window);  turtle := (0.5, 0.5, 0, TRUE);  draw move (window, x OF turtle, y OF turtle);  draw colour name(window, "white")); PROC turtle left = (REAL left turn)VOID:  heading OF turtle +:= left turn; PROC turtle right = (REAL right turn)VOID:  heading OF turtle -:= right turn; PROC turtle forward = (REAL distance)VOID:(  x OF turtle +:= distance * cos(heading OF turtle) / width * height;  y OF turtle +:= distance * sin(heading OF turtle);  IF pen down OF turtle THEN    draw line  ELSE    draw move  FI (window, x OF turtle, y OF turtle)); SKIP
File: prelude/exception.a68
# -*- coding: utf-8 -*- # COMMENT  REQUIRES :    MODE EXCEPTOBJ = UNION(VOID, MODEA, MODEB, MODEC ...);    OP FIRMSTR = (EXCEPTOBJ obj)STRING: ~END COMMENT MODE EXCEPTOBJS = [0]EXCEPTOBJ; OP STR = (EXCEPTOBJS obj)STRING: (  STRING out := "(", fs := "";  FOR this FROM LWB obj TO UPB obj DO out +:= fs+FIRMSTR obj[this]; fs:=", " OD;  out +")"); MODE EXCEPTMEND = PROC(EXCEPTOBJS #obj#,STRING #msg#)BOOL; PROC super mend = (EXCEPTOBJS obj,STRING sub exception, msg)BOOL:  ( put(stand error, ("exception/",sub exception,": ", msg," - ", STR obj, new line)); break; TRUE); PROC super break mend = (EXCEPTOBJS obj,STRING sub exception, msg)BOOL: ( super mend(obj, sub exception, msg); break; TRUE);PROC super stop mend = (EXCEPTOBJS obj,STRING sub exception, msg)BOOL: ( super mend(obj, sub exception, msg); stop; FALSE);PROC super ignore mend = (EXCEPTOBJS obj,STRING sub exception, msg)BOOL: ( #super mend(obj, sub exception, msg);# TRUE); EXCEPTMEND on undefined mend := super break mend(,"undefined",);PROC on undefined = (EXCEPTMEND undefined mend)VOID: on undefined mend := undefined mend;PROC raise undefined = (EXCEPTOBJS obj, STRING msg)VOID: IF NOT on undefined mend(obj, msg) THEN stop FI; EXCEPTMEND on value error mend := super break mend(,"value error",);PROC on value error = (EXCEPTMEND value error mend)VOID: on value error mend := value error mend;PROC raise value error = (EXCEPTOBJS obj, STRING msg)VOID: IF NOT on value error mend(obj, msg) THEN stop FI; EXCEPTMEND on bounds error mend := super break mend(,"bounds error",);PROC on bounds error = (EXCEPTMEND bounds error mend)VOID: on bounds error mend := bounds error mend;PROC raise bounds error = (EXCEPTOBJS obj, STRING msg)VOID: IF NOT on bounds error mend(obj, msg) THEN stop FI; EXCEPTMEND on tagged union error mend := super break mend(,"tagged union error",);PROC on tagged union error = (EXCEPTMEND tagged union error mend)VOID: on tagged union error mend := tagged union error mend;PROC raise tagged union error = (EXCEPTOBJS obj, STRING msg)VOID: IF NOT on tagged union error mend(obj, msg) THEN stop FI; EXCEPTMEND on untested mend := super break mend(,"untested",);PROC on untested = (EXCEPTMEND untested mend)VOID: on untested mend := untested mend;PROC raise untested = (EXCEPTOBJS obj, STRING msg)VOID: IF NOT on untested mend(obj, msg) THEN stop FI; EXCEPTMEND on unimplemented mend := super break mend(,"unimplemented",);PROC on unimplemented = (EXCEPTMEND unimplemented mend)VOID: on unimplemented mend := unimplemented mend;PROC raise unimplemented = (EXCEPTOBJS obj, STRING msg)VOID: IF NOT on unimplemented mend(obj, msg) THEN stop FI; SKIP
File: test/Dragon_curve.a68
#!/usr/bin/a68g --script ## -*- coding: utf-8 -*- # PR read "prelude/turtle_draw.a68" PR;MODE EXCEPTOBJ = FILE;OP FIRMSTR = (EXCEPTOBJ obj)STRING: "FILE"; PR read "prelude/exception.a68" PR; REAL sqrt 2 = sqrt(2), degrees = pi/180; STRUCT ( INT count, depth, current shade, upb lines, upb colours ) morph; PROC morph init = (INT depth)VOID: (  count OF morph := 0;  depth OF morph := depth;  current shade OF morph := -1;  upb lines OF morph := 2**depth;  upb colours OF morph := 16); PROC morph colour = VOID: (  INT colour sectors = 3; # RGB #  INT candidate shade = ENTIER ( count OF morph / upb lines OF morph * upb colours OF morph );  IF candidate shade /= current shade OF morph THEN    current shade OF morph := candidate shade;    REAL colour sector = colour sectors * candidate shade / upb colours OF morph - 0.5;    REAL shade = colour sector - ENTIER colour sector;    CASE ENTIER colour sector + 1 # of 3 # IN      draw colour (window, 1 - shade, shade, 0),      draw colour (window, 0, 1 - shade, shade)    OUT      draw colour (window, shade, 0, 1 - shade)    ESAC  FI;  count OF morph +:= 1); PROC dragon init = VOID: (  pen down OF turtle := FALSE;    turtle forward(23/64); turtle right(90*degrees);    turtle forward (1/8);  turtle right(90*degrees);  pen down OF turtle := TRUE); PROC dragon = (REAL in step, in length, PROC(REAL)VOID zig, zag)VOID: (  IF in step <= 0 THEN    morph colour;    turtle forward(in length)  ELSE    REAL step = in step - 1;    REAL length = in length / sqrt 2;     zig(45*degrees);    dragon(step, length, turtle right, turtle left);    zag(90*degrees);    dragon(step, length, turtle left, turtle right);    zig(45*degrees)  FI); PROC window init = VOID: (  STRING aspect; FILE f; associate(f, aspect); putf(f, ($g(-4)"x"g(-3)$, width, height));CO # depricated #  IF NOT draw device (window, "X", aspect)THEN    raise undefined(window, "cannot initialise X draw device") FI;END CO  IF open (window, "Dragon Curve", stand draw channel) = 0 THEN    raise undefined(window, "cannot open Dragon Curve window") FI;  IF NOT make device (window, "X", aspect) THEN    raise undefined(window, "cannot make device X draw device") FI); INT width = 800-15, height = 600-15; FILE window; window init;  INT cycle length = 18;  FOR snap shot TO cycle length DO    INT depth := (snap shot - 2) MOD cycle length;    turtle init; dragon init; morph init(depth);# move to initial turtle location #    dragon(depth, 7/8, turtle right, turtle left);    draw show (window);    VOID(system("sleep 1"))  OD;close (window)

Output:

 ALGOL 68 Dragon curve animated

Note: each Dragon curve is composed of many smaller dragon curves (shown in a different colour).

## AmigaE

Example code using mutual recursion can be found in Recursion Example of "A Beginner's Guide to Amiga E".

## Applesoft BASIC

Apple IIe BASIC code can be found in Thomas Bannon, "Fractals and Transformations", Mathematics Teacher, March 1991, pages 178-185. (At JSTOR.)

## Asymptote

The Asymptote source code includes an examples/dragon.asy which draws the dragon curve (four interlocking copies actually),

http://asymptote.sourceforge.net/gallery/dragon.asy
http://asymptote.sourceforge.net/gallery/dragon.pdf

As of its version 2.15 it uses the successive approximation method. Vertices are represented as an array of "pairs" (complex numbers). Between each two vertices a new vertex is is introduced so as to double the segments, repeated to a desired level.

## BASIC

Works with: QBasic
DIM SHARED angle AS DOUBLE SUB turn (degrees AS DOUBLE)    angle = angle + degrees*3.14159265/180END SUB SUB forward (length AS DOUBLE)    LINE - STEP (COS(angle)*length, SIN(angle)*length), 7END SUB SUB dragon (length AS DOUBLE, split AS INTEGER, d AS DOUBLE)    IF split=0 THEN        forward length    ELSE	turn d*45	dragon length/1.4142136, split-1, 1	turn -d*90	dragon length/1.4142136, split-1, -1	turn d*45    END IFEND SUB ' Main program SCREEN 12angle = 0PSET (150,180), 0dragon 400, 12, 1SLEEP

See also Sydney Afriat "Dragon Curves" paper for various approaches in BASIC

And TRS-80 BASIC code in Dan Rollins, "A Tiger Meets a Dragon: An examination of the mathematical properties of dragon curves and a program to print them on an IDS Paper Tiger", Byte Magazine, December 1983. (Based on generating a string of turns by appending middle turn and reversed copy. Options for the middle turn give the alternate paper folding curve and more too. The turns are then followed for the plot.)

### IS-BASIC

100 PROGRAM "Dragon.bas"110 OPTION ANGLE DEGREES120 LET SQ2=SQR(2)130 GRAPHICS HIRES 2140 SET PALETTE 0,33150 PLOT 250,360,ANGLE 0;160 CALL DC(580,0,11)170 DEF DC(D,A,LEV)180   IF LEV=0 THEN190     PLOT FORWARD D;200   ELSE210     PLOT RIGHT A;220     CALL DC(D/SQ2,45,LEV-1)230     PLOT LEFT 2*A;240     CALL DC(D/SQ2,-45,LEV-1)250     PLOT RIGHT A;260   END IF270 END DEF

## BASIC256

Image created by the BASIC-256 script
# Version without functions (for BASIC-256 ver. 0.9.6.66) graphsize 390,270 level = 18 : insize = 247		# initial valuesx = 92 : y = 94	        		# iters = 2^level		        	# total number of iterationsqiter = 510/iters			# constant for computing colorsSQ = sqrt(2) : QPI = pi/4		# constants rotation = 0 : iter = 0 : rq = 1.0	# state variablesdim rqs(level)			        # stack for rq (rotation coefficient) color whitefastgraphicsrect 0,0,graphwidth,graphheightrefreshgosub dragonrefreshimgsave "Dragon_curve_BASIC-256.png", "PNG"end dragon:	if level<=0 then 		yn = sin(rotation)*insize + y		xn = cos(rotation)*insize + x		if iter*2<iters then 			color 0,iter*qiter,255-iter*qiter		else 			color qiter*iter-255,(iters-iter)*qiter,0		end if		line x,y,xn,yn		iter = iter + 1		x = xn : y = yn		return	end if	insize = insize/SQ	rotation = rotation + rq*QPI	level = level - 1	rqs[level] = rq : rq = 1	gosub dragon	rotation = rotation - rqs[level]*QPI*2	rq = -1	gosub dragon	rq = rqs[level]	rotation = rotation + rq*QPI	level = level + 1	insize = insize*SQ	return

## BBC BASIC

      MODE 8      MOVE 800,400      GCOL 11      PROCdragon(512, 12, 1)      END       DEF PROCdragon(size, split%, d)      PRIVATE angle      IF split% = 0 THEN        DRAW BY -COS(angle)*size, SIN(angle)*size      ELSE        angle += d*PI/4        PROCdragon(size/SQR(2), split%-1, 1)        angle -= d*PI/2        PROCdragon(size/SQR(2), split%-1, -1)        angle += d*PI/4      ENDIF      ENDPROC

## Befunge

This is loosely based on the M4 predicate algorithm, only it produces a more compact ASCII output (which is also a little easier to implement), and it lets you choose the depth of the expansion rather than having to specify the coordinates of the viewing area.

In Befunge-93 the 8-bit cell size restricts you to a maximum depth of 15, but in Befunge-98 you should be able go quite a bit deeper before other limits of the implementation come into play.

" :htpeD">:#,_&>:00p:2%10p:2/:1+1>\#<1#*-#2:#\_$:1-20p510g2*-*1+610g4vv<v<| v%2\/3-1$_\#!4#:*#-\#1<\1+1:/4+1g00:\_\#$1<%2/2+1\g02\-1+%-g012\/-*<v"*/_ >!>0$#0\#$\_-10p20p::00g4/:1+1>\#<1#*-#4:#\_$1-2*3/\2%!>0$#0\#$\_--vv|+2v:\p06!*-1::p05<g00+1--g01g03\+-g01-p04+1:<0p03:-1_>>$1-\1->>:v:+1\<v~::>:1+*!60g*!#v_!\!*50g0*!40gg,::30g40g:2-#^_>>$>>:^:+1g02::\,+55_55+,@v":*v%2/2+*">~":<  ^\-1g05-*">~"/2+*"|~"-%*"|~"\/*"|~":\-*">~"/2+%*"|~"\/*<^<:>60p\:"~>"*+2/2%60g+2%70p:"kI"*+2/2%60p\:"kI"*+2/2%60g+2%-\70g-"~|"**+"}"^
Output:
Depth: 9

_       _
|_|_    |_|_
_   _|_|_   _|_|
|_|_| |_| |_|_|_                     _   _
_|        _|_|_|    _             _| |_|_|
|_        |_| |_    |_|_          |_    |_   _
|_|          _|_   _|_|                _|_|_|
_|_|_|_|_|_                |_|_|
_|_|_|_|_|_|_|    _       _   _|
|_| |_|_|_|_|_    |_|_    |_|_|_   _
_|_|_|_|_|_   _|_|_   _|_|_|_|_|
_|_|_|_| |_| |_|_|_|_|_| |_| |_|
_|_|_|_|        _|_|_|_|
|_| |_|_   _    |_| |_|_   _
_|_|_|_|        _|_|_|_|
|_| |_|         |_| |_|

## C

See: Dragon curve/C

### C by IFS Drawing

C code that writes PNM of dragon curve. run as a.out [depth] > dragon.pnm. Sample image was with depth 9 (512 pixel length).

#include <stdio.h>#include <stdlib.h>#include <string.h>#include <math.h> /* x, y: coordinates of current point; dx, dy: direction of movement. * Think turtle graphics.  They are divided by scale, so as to keep * very small coords/increments without losing precission. clen is * the path length travelled, which should equal to scale at the end * of the curve. */long long x, y, dx, dy, scale, clen;typedef struct { double r, g, b; } rgb;rgb ** pix; /* for every depth increase, rotate 45 degrees and scale up by sqrt(2) * Note how coords can still be represented by integers. */void sc_up(){	long long tmp = dx - dy; dy = dx + dy; dx = tmp;	scale *= 2; x *= 2; y *= 2;} /* Hue changes from 0 to 360 degrees over entire length of path; Value * oscillates along the path to give some contrast between segments * close to each other spatially.  RGB derived from HSV gets *added* * to each pixel reached; they'll be dealt with later. */void h_rgb(long long x, long long y){	rgb *p = &pix[y][x]; #	define SAT 1	double h = 6.0 * clen / scale;	double VAL = 1 - (cos(3.141592653579 * 64 * clen / scale) - 1) / 4;	double c = SAT * VAL;	double X = c * (1 - fabs(fmod(h, 2) - 1)); 	switch((int)h) {	case 0: p->r += c; p->g += X; return;	case 1:	p->r += X; p->g += c; return;	case 2: p->g += c; p->b += X; return;	case 3: p->g += X; p->b += c; return;	case 4: p->r += X; p->b += c; return;	default:		p->r += c; p->b += X;	}} /* string rewriting.  No need to keep the string itself, just execute * its instruction recursively. */void iter_string(const char * str, int d){	long tmp;#	define LEFT  tmp = -dy; dy = dx; dx = tmp#	define RIGHT tmp = dy; dy = -dx; dx = tmp	while (*str != '\0') {		switch(*(str++)) {		case 'X':	if (d) iter_string("X+YF+", d - 1); continue;		case 'Y':	if (d) iter_string("-FX-Y", d - 1); continue;		case '+':	RIGHT; continue;		case '-':	LEFT;  continue;		case 'F':                        /* draw: increment path length; add color; move. Here                         * is why the code does not allow user to choose arbitrary                         * image size: if it's not a power of two, aliasing will                         * occur and grid-like bright or dark lines will result                         * when normalized later.  It can be gotten rid of, but that                         * involves computing multiplicative order and would be a huge                         * bore.                         */				clen ++;				h_rgb(x/scale, y/scale);				x += dx; y += dy;				continue;		}	}} void dragon(long leng, int depth){	long i, d = leng / 3 + 1;	long h = leng + 3, w = leng + d * 3 / 2 + 2; 	/* allocate pixel buffer */	rgb *buf = malloc(sizeof(rgb) * w * h);	pix = malloc(sizeof(rgb *) * h);	for (i = 0; i < h; i++)		pix[i] = buf + w * i;	memset(buf, 0, sizeof(rgb) * w * h);         /* init coords; scale up to desired; exec string */	x = y = d; dx = leng; dy = 0; scale = 1; clen = 0;	for (i = 0; i < depth; i++) sc_up();	iter_string("FX", depth); 	/* write color PNM file */	unsigned char *fpix = malloc(w * h * 3);	double maxv = 0, *dbuf = (double*)buf;         /* find highest value among pixels; normalize image according         * to it.  Highest value would be at points most travelled, so         * this ends up giving curve edge a nice fade -- it's more apparaent         * if we increase iteration depth by one or two.         */	for (i = 3 * w * h - 1; i >= 0; i--)		if (dbuf[i] > maxv) maxv = dbuf[i];	for (i = 3 * h * w - 1; i >= 0; i--)		fpix[i] = 255 * dbuf[i] / maxv; 	printf("P6\n%ld %ld\n255\n", w, h);	fflush(stdout); /* printf and fwrite may treat buffer differently */	fwrite(fpix, h * w * 3, 1, stdout);} int main(int c, char ** v){	int size, depth; 	depth  = (c > 1) ? atoi(v[1]) : 10;	size = 1 << depth; 	fprintf(stderr, "size: %d depth: %d\n", size, depth);	dragon(size, depth * 2); 	return 0;}

## C++

This program will generate the curve and save it to your hard drive.

 #include <windows.h>#include <iostream> //-----------------------------------------------------------------------------------------using namespace std; //-----------------------------------------------------------------------------------------const int BMP_SIZE = 800, NORTH = 1, EAST = 2, SOUTH = 4, WEST = 8, LEN = 1; //-----------------------------------------------------------------------------------------class myBitmap{public:    myBitmap() : pen( NULL ), brush( NULL ), clr( 0 ), wid( 1 ) {}    ~myBitmap()    {	DeleteObject( pen ); DeleteObject( brush );	DeleteDC( hdc ); DeleteObject( bmp );    }     bool create( int w, int h )    {	BITMAPINFO bi;	ZeroMemory( &bi, sizeof( bi ) );	bi.bmiHeader.biSize        = sizeof( bi.bmiHeader );	bi.bmiHeader.biBitCount    = sizeof( DWORD ) * 8;	bi.bmiHeader.biCompression = BI_RGB;	bi.bmiHeader.biPlanes      = 1;	bi.bmiHeader.biWidth       =  w;	bi.bmiHeader.biHeight      = -h; 	HDC dc = GetDC( GetConsoleWindow() );	bmp = CreateDIBSection( dc, &bi, DIB_RGB_COLORS, &pBits, NULL, 0 );	if( !bmp ) return false; 	hdc = CreateCompatibleDC( dc );	SelectObject( hdc, bmp );	ReleaseDC( GetConsoleWindow(), dc ); 	width = w; height = h;	return true;    }     void clear( BYTE clr = 0 )    {	memset( pBits, clr, width * height * sizeof( DWORD ) );    }     void setBrushColor( DWORD bClr )    {	if( brush ) DeleteObject( brush );	brush = CreateSolidBrush( bClr );	SelectObject( hdc, brush );    }     void setPenColor( DWORD c )    {	clr = c; createPen();    }     void setPenWidth( int w )    {	wid = w; createPen();    }     void saveBitmap( string path )     {	BITMAPFILEHEADER fileheader;	BITMAPINFO       infoheader;	BITMAP           bitmap;	DWORD            wb; 	GetObject( bmp, sizeof( bitmap ), &bitmap );	DWORD* dwpBits = new DWORD[bitmap.bmWidth * bitmap.bmHeight]; 	ZeroMemory( dwpBits, bitmap.bmWidth * bitmap.bmHeight * sizeof( DWORD ) );	ZeroMemory( &infoheader, sizeof( BITMAPINFO ) );	ZeroMemory( &fileheader, sizeof( BITMAPFILEHEADER ) ); 	infoheader.bmiHeader.biBitCount = sizeof( DWORD ) * 8;	infoheader.bmiHeader.biCompression = BI_RGB;	infoheader.bmiHeader.biPlanes = 1;	infoheader.bmiHeader.biSize = sizeof( infoheader.bmiHeader );	infoheader.bmiHeader.biHeight = bitmap.bmHeight;	infoheader.bmiHeader.biWidth = bitmap.bmWidth;	infoheader.bmiHeader.biSizeImage = bitmap.bmWidth * bitmap.bmHeight * sizeof( DWORD ); 	fileheader.bfType    = 0x4D42;	fileheader.bfOffBits = sizeof( infoheader.bmiHeader ) + sizeof( BITMAPFILEHEADER );	fileheader.bfSize    = fileheader.bfOffBits + infoheader.bmiHeader.biSizeImage; 	GetDIBits( hdc, bmp, 0, height, ( LPVOID )dwpBits, &infoheader, DIB_RGB_COLORS ); 	HANDLE file = CreateFile( path.c_str(), GENERIC_WRITE, 0, NULL, CREATE_ALWAYS, FILE_ATTRIBUTE_NORMAL, NULL );	WriteFile( file, &fileheader, sizeof( BITMAPFILEHEADER ), &wb, NULL );	WriteFile( file, &infoheader.bmiHeader, sizeof( infoheader.bmiHeader ), &wb, NULL );	WriteFile( file, dwpBits, bitmap.bmWidth * bitmap.bmHeight * 4, &wb, NULL );	CloseHandle( file ); 	delete [] dwpBits;    }     HDC getDC() const     { return hdc; }    int getWidth() const  { return width; }    int getHeight() const { return height; } private:    void createPen()    {	if( pen ) DeleteObject( pen );	pen = CreatePen( PS_SOLID, wid, clr );	SelectObject( hdc, pen );    }     HBITMAP bmp;    HDC     hdc;    HPEN    pen;    HBRUSH  brush;    void    *pBits;    int     width, height, wid;    DWORD   clr;};//-----------------------------------------------------------------------------------------class dragonC{public:    dragonC() { bmp.create( BMP_SIZE, BMP_SIZE ); dir = WEST; }    void draw( int iterations ) { generate( iterations ); draw(); } private:    void generate( int it )    {	generator.push_back( 1 );	string temp; 	for( int y = 0; y < it - 1; y++ )	{	    temp = generator; temp.push_back( 1 );	    for( string::reverse_iterator x = generator.rbegin(); x != generator.rend(); x++ )		temp.push_back( !( *x ) ); 	    generator = temp;	}    }     void draw()    {	HDC dc = bmp.getDC();	unsigned int clr[] = { 0xff, 0xff00, 0xff0000, 0x00ffff };	int mov[] = { 0, 0, 1, -1, 1, -1, 1, 0 }; int i = 0; 	for( int t = 0; t < 4; t++ )	{	    int a = BMP_SIZE / 2, b = a; a += mov[i++]; b += mov[i++];	    MoveToEx( dc, a, b, NULL ); 	    bmp.setPenColor( clr[t] );	    for( string::iterator x = generator.begin(); x < generator.end(); x++ )	    {		switch( dir )		{		    case NORTH:			if( *x ) { a += LEN; dir = EAST; }			else { a -= LEN; dir = WEST; }						    break;		    case EAST:			if( *x ) { b += LEN; dir = SOUTH; }			else { b -= LEN; dir = NORTH; }		    break;		    case SOUTH:			if( *x ) { a -= LEN; dir = WEST; }			else { a += LEN; dir = EAST; }		    break;		    case WEST:			if( *x ) { b -= LEN; dir = NORTH; }			else { b += LEN; dir = SOUTH; }		}	        LineTo( dc, a, b );	    }	}	// !!! change this path !!!	bmp.saveBitmap( "f:/rc/dragonCpp.bmp" );    }     int dir;    myBitmap bmp;    string generator;};//-----------------------------------------------------------------------------------------int main( int argc, char* argv[] ){    dragonC d; d.draw( 17 );    return system( "pause" );}//----------------------------------------------------------------------------------------- 

## C#

Translation of: Java
using System;using System.Collections.Generic;using System.Drawing;using System.Drawing.Drawing2D;using System.Windows.Forms; public class DragonCurve : Form{    private List<int> turns;    private double startingAngle, side;     public DragonCurve(int iter)    {        Size = new Size(800, 600);        StartPosition = FormStartPosition.CenterScreen;        DoubleBuffered = true;        BackColor = Color.White;         startingAngle = -iter * (Math.PI / 4);        side = 400 / Math.Pow(2, iter / 2.0);         turns = getSequence(iter);    }     private List<int> getSequence(int iter)    {        var turnSequence = new List<int>();        for (int i = 0; i < iter; i++)        {            var copy = new List<int>(turnSequence);            copy.Reverse();            turnSequence.Add(1);            foreach (int turn in copy)            {                turnSequence.Add(-turn);            }        }        return turnSequence;    }     protected override void OnPaint(PaintEventArgs e)    {        base.OnPaint(e);        e.Graphics.SmoothingMode = SmoothingMode.AntiAlias;         double angle = startingAngle;        int x1 = 230, y1 = 350;        int x2 = x1 + (int)(Math.Cos(angle) * side);        int y2 = y1 + (int)(Math.Sin(angle) * side);        e.Graphics.DrawLine(Pens.Black, x1, y1, x2, y2);        x1 = x2;        y1 = y2;        foreach (int turn in turns)        {            angle += turn * (Math.PI / 2);            x2 = x1 + (int)(Math.Cos(angle) * side);            y2 = y1 + (int)(Math.Sin(angle) * side);            e.Graphics.DrawLine(Pens.Black, x1, y1, x2, y2);            x1 = x2;            y1 = y2;        }    }     [STAThread]    static void Main()    {        Application.Run(new DragonCurve(14));    }}

## COBOL

Works with: GnuCOBOL
         >>SOURCE FORMAT FREE*> This code is dedicated to the public domainidentification division.program-id. dragon.environment division.configuration section.repository. function all intrinsic.data division.working-storage section.01  segment-length pic 9 value 2.01  mark pic x value '.'.01  segment-count pic 9999 value 513. 01  segment pic 9999.01  point pic 9999 value 1.01  point-max pic 9999.01  point-lim pic 9999 value 8192.01  dragon-curve.    03  filler occurs 8192.        05  ydragon pic s9999.        05  xdragon pic s9999. 01  x pic s9999 value 1.01  y pic S9999 value 1. 01  xdelta pic s9 value 1. *> start pointing east01  ydelta pic s9 value 0. 01  x-max pic s9999 value -9999.01  x-min pic s9999 value 9999.01  y-max pic s9999 value -9999.01  y-min pic s9999 value 9999. 01  n pic 9999.01  r pic 9. 01  xupper pic s9999.01  yupper pic s9999. 01  window-line-number pic 99.01  window-width pic 99 value 64.01  window-height pic 99 value 22.01  window.    03  window-line occurs 22.        05  window-point occurs 64 pic x. 01  direction pic x. procedure division.start-dragon.     if segment-count * segment-length > point-lim        *> too many segments for the point-table        compute segment-count = point-lim / segment-length    end-if     perform varying segment from 1 by 1    until segment > segment-count         *>===========================================        *> segment = n * 2 ** b        *> if mod(n,4) = 3, turn left else turn right        *>===========================================         *> calculate the turn        divide 2 into segment giving n remainder r        perform until r <> 0            divide 2 into n giving n remainder r        end-perform        divide 2 into n giving n remainder r         *> perform the turn        evaluate r also xdelta also ydelta        when 0 also 1 also 0  *> turn right from east        when 1 also -1 also 0 *> turn left from west            *> turn to south            move 0 to xdelta            move 1 to ydelta        when 1 also 1 also 0  *> turn left from east        when 0 also -1 also 0 *> turn right from west            *> turn to north            move 0 to xdelta            move -1 to ydelta        when 0 also 0 also 1  *> turn right from south        when 1 also 0 also -1 *> turn left from north            *> turn to west            move 0 to ydelta            move -1 to xdelta        when 1 also 0 also 1  *> turn left from south        when 0 also 0 also -1 *> turn right from north            *> turn to east            move 0 to ydelta            move 1 to xdelta        end-evaluate         *> plot the segment points        perform segment-length times            add xdelta to x            add ydelta to y             move x to xdragon(point)            move y to ydragon(point)             add 1 to point        end-perform         *> update the limits for the display        compute x-max = max(x, x-max)        compute x-min = min(x, x-min)        compute y-max = max(y, y-max)        compute y-min = min(y, y-min)        move point to point-max     end-perform     *>==========================================    *> display the curve    *> hjkl corresponds to left, up, down, right    *> anything else ends the program    *>==========================================     move 1 to yupper xupper     perform with test after    until direction <> 'h' and 'j' and 'k' and 'l'         *>==========================================        *> (yupper,xupper) maps to window-point(1,1)        *>==========================================         *> move the window        evaluate true        when direction = 'h' *> move window left        and xupper > x-min + window-width           subtract 1 from xupper        when direction = 'j' *> move window up        and yupper < y-max - window-height           add 1 to yupper        when direction = 'k' *> move window down        and yupper > y-min + window-height           subtract 1 from yupper        when direction = 'l' *> move window right        and xupper < x-max - window-width            add 1 to xupper        end-evaluate         *> plot the dragon points in the window        move spaces to window        perform varying point from 1 by 1        until point > point-max            if ydragon(point) >= yupper and < yupper + window-height            and xdragon(point) >= xupper and < xupper + window-width                *> we're in the window                compute y = ydragon(point) - yupper + 1                compute x =  xdragon(point) - xupper + 1                move mark to window-point(y, x)            end-if         end-perform          *> display the window         perform varying window-line-number from 1 by 1         until window-line-number > window-height             display window-line(window-line-number)         end-perform          *> get the next window move or terminate         display 'hjkl?' with no advancing         accept direction    end-perform     stop run    .end program dragon.
Output:
                  . . .         . . . .
....... ... .........
. . . . . . . . .
... ...................
. . . . . . . . . . .
....................... ...
. . . . . . . . . . . . .
... ...........................
. . . . . . . . . . . . . . .
..................... ... ...
. . . . . . . . .
..... .............
. .     . . . . .
.....   ........... ...
. .     . . . . . . .
...   ...............
. . . . . . .
..... ... ...
.
... ...
. . .
....... ...
hjkl?q

## Common Lisp

Library: CLIM

This implementation uses nested transformations rather than turtle motions. with-scaling, etc. establish transformations for the drawing which occurs within them.

The recursive dragon-part function draws a curve connecting (0,0) to (1,0); if depth is 0 then the curve is a straight line. bend-direction is either 1 or -1 to specify whether the deviation from a straight line should be to the right or left.

(defpackage #:dragon  (:use #:clim-lisp #:clim)  (:export #:dragon #:dragon-part))(in-package #:dragon) (defun dragon-part (depth bend-direction)  (if (zerop depth)      (draw-line* *standard-output* 0 0 1 0)      (with-scaling (t (/ (sqrt 2)))        (with-rotation (t (* pi -1/4 bend-direction))          (dragon-part (1- depth) 1)          (with-translation (t 1 0)            (with-rotation (t (* pi 1/2 bend-direction))              (dragon-part (1- depth) -1))))))) (defun dragon (&optional (depth 7) (size 100))  (with-room-for-graphics ()    (with-scaling (t size)      (dragon-part depth 1))))

## D

### Text mode

A textual version of Dragon curve.
The Dragon curve drawn using an L-system.

• variables : X Y F
• constants : + −
• start  : FX
• rules  : (X → X+YF+),(Y → -FX-Y)
• angle  : 90°
import std.stdio, std.string; struct Board {    enum char spc = ' ';    char[][] b = [[' ']]; // Set at least 1x1 board.    int shiftx, shifty;     void clear() pure nothrow {        shiftx = shifty = 0;        b = [['\0']];    }     void check(in int x, in int y) pure nothrow {        while (y + shifty < 0) {            auto newr = new char[b[0].length];            newr[] = spc;            b = newr ~ b;            shifty++;        }         while (y + shifty >= b.length) {            auto newr = new char[b[0].length];            newr[] = spc;            b ~= newr;        }         while (x + shiftx < 0) {            foreach (ref c; b)                c = [spc] ~ c;            shiftx++;        }         while (x + shiftx >= b[0].length)            foreach (ref c; b)                c ~= [spc];    }     char opIndexAssign(in char value, in int x, in int y)    pure nothrow {        check(x, y);        b[y + shifty][x + shiftx] = value;        return value;    }     string toString() const pure {        return format("%-(%s\n%)", b);    }} struct Turtle {    static struct TState {        int[2] xy;        int heading;    }     enum int[2][] dirs = [[1, 0],  [1,   1], [0,  1], [-1,  1],                          [-1, 0], [-1, -1], [0, -1],  [1, -1]];    enum string trace = r"-\|/-\|/";    TState t;     void reset() pure nothrow {        t = typeof(t).init;    }     void turn(in int dir) pure nothrow {        t.heading = (t.heading + 8 + dir) % 8;    }     void forward(ref Board b) pure nothrow {        with (t) {            xy[] += dirs[heading][];            b[xy[0], xy[1]] = trace[heading];            xy[] += dirs[heading][];            b[xy[0], xy[1]] = b.spc;        }    }} void dragonX(in int n, ref Turtle t, ref Board b) pure nothrow {    if (n >= 0) { // X -> X+YF+        dragonX(n - 1, t, b);        t.turn(2);        dragonY(n - 1, t, b);        t.forward(b);        t.turn(2);    }} void dragonY(in int n, ref Turtle t, ref Board b) pure nothrow {    if (n >= 0) { // Y -> -FX-Y        t.turn(-2);        t.forward(b);        dragonX(n - 1, t, b);        t.turn(-2);        dragonY(n - 1, t, b);    }} void main() {    Turtle t;    Board b;                      // Seed : FX    t.forward(b);     // <- F    dragonX(7, t, b); // <- X    writeln(b);}
Output:
           -   -           -   -
| | | |         | | | |
- - - -         - - - -
| | | |         | | | |
-   - -   -     -   - -   -
| | | |         | | | |
- - - -         - - - -
| | | |         | | | |
-   -   - - - - -   -   - - - -
| | | | | | | | | | | | | | | |
- - - - -   - - -   - - - - - -
| | | | |     | |     | | | | |
-   - - -     - -     - - - - -   -
| | |     | |     | | | | | | |
-   -       -     - - - - - - -
|                 | | | | | | |
- -                 - - - - - -
| | |                 | | | | |
- - -                 - -   - -           -
| | |                 | |     |           | |
-   -     -           - -     -   -         -
|     |           | |     | | |         |
- -   -             -     - - -         -
| | | |                   | | |         |
-   -                     - - -   -   - -
| | | | | | | |
- -   - - -   -
| |     | |
- -     - -
| |     | |
-       -     

### PostScript Output Version

import std.stdio, std.string; string drx(in size_t n) pure nothrow {    return n ? (drx(n - 1) ~ " +" ~ dry(n - 1) ~ " f +") : "";} string dry(in size_t n) pure nothrow {    return n ? (" - f" ~ drx(n - 1) ~ " -" ~ dry(n - 1)) : "";} string dragonCurvePS(in size_t n) pure nothrow {    return ["0 setlinewidth 300 400 moveto",            "/f{2 0 rlineto}def/+{90 rotate}def/-{-90 rotate}def\n",            "f", drx(n), " stroke showpage"].join();} void main() {    writeln(dragonCurvePS(9)); // Increase this for a bigger curve.}

### On a Bitmap

This uses the modules from the bresenhams line algorithm and Grayscale Image tasks.

First a small "turtle.d" module, useful for other tasks:

module turtle; import bitmap_bresenhams_line_algorithm, grayscale_image, std.math; // Minimal turtle graphics.struct Turtle {    real x = 100, y = 100, angle = -90;     void left(in real a) pure nothrow { angle -= a; }    void right(in real a) pure nothrow { angle += a; }     void forward(Color)(Image!Color img, in real len) pure nothrow {        immutable r = angle * (PI / 180.0);        immutable dx = r.cos * len;        immutable dy = r.sin * len;        img.drawLine(cast(uint)x, cast(uint)y,                     cast(uint)(x + dx), cast(uint)(y + dy),                     Color.white);        x += dx;        y += dy;    }}

Then the implementation is simple:

Translation of: PicoLisp
import grayscale_image, turtle; void drawDragon(Color)(Image!Color img, ref Turtle t, in uint depth,                       in real dir, in uint step) {    if (depth == 0)        return t.forward(img, step);    t.right(dir);    img.drawDragon(t, depth - 1, 45.0, step);    t.left(dir * 2);    img.drawDragon(t, depth - 1, -45.0, step);    t.right(dir);} void main() {    auto img = new Image!Gray(500, 700);    auto t = Turtle(180, 510, -90);    img.drawDragon(t, 14, 45.0, 3);    img.savePGM("dragon_curve.pgm");}

## Elm

import Color exposing (..)import Collage exposing (..)import Element exposing (..)import Time exposing (..)import Html exposing (..)import Html.App exposing (program)  type alias Point = (Float, Float) type alias Model =  { points : List Point  , level : Int  , frame : Int  } maxLevel = 12frameCount = 100 type Msg = Tick Time init : (Model,Cmd Msg)init = ( { points = [(-200.0, -70.0), (200.0, -70.0)]         , level = 0          , frame = 0         }       , Cmd.none ) -- New point between two existing points.  Offset to left or rightnewPoint : Point -> Point -> Float -> PointnewPoint  (x0,y0) (x1,y1) offset =   let (vx, vy) = ((x1 - x0) / 2.0, (y1 - y0) / 2.0)       (dx, dy) = (-vy * offset , vx * offset )  in  (x0 + vx + dx, y0 + vy + dy) --offset from midpoint  -- Insert between existing points. Offset to left or right side.newPoints : Float -> List Point -> List PointnewPoints offset points =   case points of    [] -> []    [p0] -> [p0]      p0::p1::rest -> p0 :: newPoint p0 p1 offset :: newPoints -offset (p1::rest) update : Msg -> Model -> (Model, Cmd Msg)update _ model =   let mo = if (model.level == maxLevel)           then model           else let nextFrame = model.frame + 1                in if (nextFrame == frameCount)                    then { points = newPoints 1.0 model.points                         , level = model.level+1                        , frame = 0                        }                   else { model | frame = nextFrame                        }  in (mo, Cmd.none) -- break a list up into n equal sized lists.breakupInto : Int -> List a -> List (List a)breakupInto n ls =     let segmentCount = (List.length ls) - 1         breakup n ls = case ls of          [] -> []          _ -> List.take (n+1) ls :: breakup n (List.drop n ls)    in if n > segmentCount        then [ls]       else breakup (segmentCount // n) ls view : Model -> Html Msgview model =   let offset = toFloat (model.frame) / toFloat frameCount      colors = [red, orange, green, blue]   in toHtml        <| layers            [ collage 700 500              (model.points                 |> newPoints offset                |> breakupInto (List.length colors) -- for coloring                |> List.map path                 |> List.map2 (\color path -> traced (solid color) path ) colors )              , show model.level            ] subscriptions : Model -> Sub Msgsubscriptions _ =     Time.every (5*millisecond) Tick main =  program       { init = init      , view = view      , update = update      , subscriptions = subscriptions      }

## Emacs Lisp

Drawing ascii art characters into a buffer using picture-mode

(require 'cl) ;; Emacs 22 and earlier for ignore-errors' (defun dragon-ensure-line-above ()  "If point is in the first line of the buffer then insert a new line above."  (when (= (line-beginning-position) (point-min))    (save-excursion      (goto-char (point-min))      (insert "\n")))) (defun dragon-ensure-column-left ()  "If point is in the first column then insert a new column to the left.This is designed for use in picture-mode'."  (when (zerop (current-column))    (save-excursion      (goto-char (point-min))      (insert " ")      (while (= 0 (forward-line 1))        (insert " ")))    (picture-forward-column 1))) (defun dragon-insert-char (char len)  "Insert CHAR repeated LEN many times.After each CHAR point move in the current picture-mode'direction (per picture-set-motion' etc). This is the same as picture-insert' except in column 0 or row 0a new row or column is inserted to make room, with existingbuffer contents shifted down or right."   (dotimes (i len)    (dragon-ensure-line-above)    (dragon-ensure-column-left)    (picture-insert char 1))) (defun dragon-bit-above-lowest-0bit (n)  "Return the bit above the lowest 0-bit in N.For example N=43 binary \"101011\" has lowest 0-bit at \"...0..\"and the bit above that is \"..1...\" so return 8 which is thatbit."  (logand n (1+ (logxor n (1+ n))))) (defun dragon-next-turn-right-p (n)  "Return non-nil if the dragon curve should turn right after segment N.Segments are numbered from N=0 for the first, so calling with N=0is whether to turn right after drawing that N=0 segment."  (zerop (dragon-bit-above-lowest-0bit n))) (defun dragon-picture (len step)  "Draw the dragon curve in a *dragon* buffer.LEN is the number of segments of the curve to draw.STEP is the length of each segment, in characters. Any LEN can be given but a power-of-2 such as 256 shows theself-similar nature of the curve. If STEP >= 2 then the segments are lines using \"-\" or \"|\"characters (picture-rectangle-h' and picture-rectangle-v').If STEP=1 then only \"+\" corners. There's a sit-for' delay in the drawing loop to draw the curveprogressively on screen."   (interactive (list (read-number "Length of curve " 256)                     (read-number "Each step size " 3)))  (unless (>= step 1)    (error "Step length must be >= 1"))   (switch-to-buffer "*dragon*")  (erase-buffer)  (ignore-errors ;; if already in picture-mode    (picture-mode))   (dotimes (n len)  ;; n=0 to len-1, inclusive    (dragon-insert-char ?+ 1)  ;; corner char    (dragon-insert-char (if (zerop picture-vertical-step)                                    picture-rectangle-h picture-rectangle-v)                                (1- step))  ;; line chars     (if (dragon-next-turn-right-p n)        ;; turn right        (picture-set-motion (- picture-horizontal-step) picture-vertical-step)      ;; turn left      (picture-set-motion picture-horizontal-step (- picture-vertical-step)))     ;; delay to display the drawing progressively    (sit-for .01))   (picture-insert ?+ 1) ;; endpoint  (picture-mode-exit)  (goto-char (point-min))) (dragon-picture 128 2)
     +-+ +-+
| | | |
+-+-+ +-+
|     |
+-+ +-+   +-+
| | |
+-+-+-+
| | |
+-+-+
|
+-+ +-+     +-+     +-+
| | |     | |     | |
+-+ +-+-+-+   +-+-+   +-+-+
| | | | |     | |     | |
+-+-+-+-+-+ +-+-+-+ +-+-+-+ +-+
| | | | | | | | | | | | | | |
+-+ +-+ +-+-+-+-+-+ +-+ +-+-+
| | | |         |
+-+-+-+-+       +-+
| | | |         |
+-+ +-+-+ +-+     + +-+
| | | |           | |
+-+-+-+-+         +-+
| | | |
+-+ +-+

## ERRE

Graphic solution with PC.LIB library

 PROGRAM DRAGON !! for rosettacode.org! !$DYNAMICDIM RQS[0] !$INCLUDE="PC.LIB" PROCEDURE DRAGON        IF LEVEL<=0 THEN                YN=SIN(ROTATION)*INSIZE+Y                XN=COS(ROTATION)*INSIZE+X                LINE(X,Y,XN,YN,12,FALSE)                ITER=ITER+1                X=XN Y=YN                EXIT PROCEDURE        END IF        INSIZE=INSIZE/SQ        ROTATION=ROTATION+RQ*QPI        LEVEL=LEVEL-1        RQS[LEVEL]=RQ        RQ=1 DRAGON        ROTATION=ROTATION-RQS[LEVEL]*QPI*2        RQ=-1 DRAGON        RQ=RQS[LEVEL]        ROTATION=ROTATION+RQ*QPI        LEVEL=LEVEL+1        INSIZE=INSIZE*SQEND PROCEDURE BEGIN        SCREEN(9)         LEVEL=12 INSIZE=287        ! initial values        X=200 Y=120                !         SQ=SQR(2)  QPI=ATN(1)      ! constants        ROTATION=0 ITER=0 RQ=1     ! state variables        !$DIM RQS[LEVEL] ! stack for RQ (ROTATION coefficient) LINE(0,0,639,349,14,TRUE) DRAGON GET(A$)END PROGRAM 

## F#

Using for visualization:
open System.Windowsopen System.Windows.Media let m = Matrix(0.0, 0.5, -0.5, 0.0, 0.0, 0.0) let step segs =  seq { for a: Point, b: Point in segs do          let x = a + 0.5 * (b - a) + (b - a) * m          yield! [a, x; b, x] } let rec nest n f x =  if n=0 then x else nest (n-1) f (f x) [<System.STAThread>]do  let path = Shapes.Path(Stroke=Brushes.Black, StrokeThickness=0.001)  path.Data <-    PathGeometry      [ for a, b in nest 13 step (seq [Point(0.0, 0.0), Point(1.0, 0.0)]) ->          PathFigure(a, [(LineSegment(b, true) :> PathSegment)], false) ]  (Application()).Run(Window(Content=Controls.Viewbox(Child=path))) |> ignore

## Factor

A translation of the BASIC example, using OpenGL, drawing with HSV coloring similar to the C example.

 USING: accessors colors colors.hsv fry kernel locals mathmath.constants math.functions opengl.gl typed ui ui.gadgetsui.gadgets.canvas ui.render ; IN: dragon CONSTANT: depth 12 TUPLE: turtle    { angle fixnum }    { color float }    { x float }    { y float } ; TYPED: nxt-color ( turtle: turtle -- turtle )    [ [ 360 2 depth ^ /f + ] keep      1.0 1.0 1.0 <hsva> >rgba-components glColor4d    ] change-color ; inline TYPED: draw-fwd ( x1: float y1: float x2: float y2: float -- )    GL_LINES glBegin glVertex2d glVertex2d glEnd ; inline TYPED:: fwd ( turtle: turtle l: float -- )    turtle x>>    turtle y>>    turtle angle>> pi * 180 / :> ( x y angle )    l angle [ cos * x + ] [ sin * y + ] 2bi :> ( dx dy )    turtle x y dx dy [ draw-fwd ] 2keep [ >>x ] [ >>y ] bi* drop ; inline TYPED: trn ( turtle: turtle d: fixnum -- turtle )    '[ _ + ] change-angle ; inline TYPED:: dragon' ( turtle: turtle l: float s: fixnum d: fixnum -- )    s zero? [        turtle nxt-color l fwd ! don't like this drop    ] [        turtle d  45 * trn l 2 sqrt / s 1 -  1 dragon'        turtle d -90 * trn l 2 sqrt / s 1 - -1 dragon'        turtle d  45 * trn drop    ] if ; : dragon ( -- )    0 0 150 180 turtle boa 400 depth 1 dragon' ; TUPLE: dragon-canvas < canvas ; M: dragon-canvas draw-gadget* [ drop dragon ] draw-canvas ;M: dragon-canvas pref-dim* drop { 640 480 } ; MAIN-WINDOW: dragon-window { { title "Dragon Curve" } }    dragon-canvas new-canvas >>gadgets ; MAIN: dragon-window 

## Forth

Works with: bigFORTH
include turtle.fs 2 value dragon-step : dragon ( depth dir -- )  over 0= if dragon-step fd  2drop exit then  dup rt  over 1-  45 recurse  dup 2* lt  over 1- -45 recurse  rt drop ; home clear10 45 dragon
Works with: 4tH

Basically the same code as the BigForth version.

Output png
include lib/graphics.4thinclude lib/gturtle.4th 2 constant dragon-step : dragon ( depth dir -- )  over 0= if dragon-step forward 2drop exit then  dup right  over 1-  45 recurse  dup 2* left  over 1- -45 recurse  right drop ; 150 pic_width !210 pic_height !color_image clear-screen 50 95 turtle!xpendown 13 45 dragons" 4tHdragon.ppm" save_image

## Gnuplot

### Version #1.

Implemented by "parametric" mode running an index t through the desired number of curve segments with X,Y position calculated for each. The "lines" plot joins them up.

# Return the position of the highest 1-bit in n.# The least significant bit is position 0.# For example n=13 is binary "1101" and the high bit is pos=3.# If n==0 then the return is 0.# Arranging the test as n>=2 avoids infinite recursion if n==NaN (any# comparison involving NaN is always false).#high_bit_pos(n) = (n>=2 ? 1+high_bit_pos(int(n/2)) : 0) # Return 0 or 1 for the bit at position "pos" in n.# pos==0 is the least significant bit.#bit(n,pos) = int(n / 2**pos) & 1 # dragon(n) returns a complex number which is the position of the# dragon curve at integer point "n".  n=0 is the first point and is at# the origin {0,0}.  Then n=1 is at {1,0} which is x=1,y=0, etc.  If n# is not an integer then the point returned is for int(n).## The calculation goes by bits of n from high to low.  Gnuplot doesn't# have iteration in functions, but can go recursively from# pos=high_bit_pos(n) down to pos=0, inclusive.## mul() rotates by +90 degrees (complex "i") at bit transitions 0->1# or 1->0.  add() is a vector (i+1)**pos for each 1-bit, but turned by# factor "i" when in a "reversed" section of curve, which is when the# bit above is also a 1-bit.#dragon(n) = dragon_by_bits(n, high_bit_pos(n))dragon_by_bits(n,pos) \  = (pos>=0 ? add(n,pos) + mul(n,pos)*dragon_by_bits(n,pos-1)  : 0) add(n,pos) = (bit(n,pos) ? (bit(n,pos+1) ? {0,1} * {1,1}**pos   \                                         :         {1,1}**pos)  \              : 0)mul(n,pos) = (bit(n,pos) == bit(n,pos+1) ? 1 : {0,1}) # Plot the dragon curve from 0 to "length" with line segments.# "trange" and "samples" are set so the parameter t runs through# integers t=0 to t=length inclusive.## Any trange works, it doesn't have to start at 0.  But must have# enough "samples" that all integers t in the range are visited,# otherwise vertices in the curve would be missed.#length=256set trange [0:length]set samples length+1set parametricset key offplot real(dragon(t)),imag(dragon(t)) with lines

### Version #2.

Note
• plotdcf.gp file-functions for the load command is the only possible imitation of the fine functions in the gnuplot.
Works with: gnuplot version 5.0 (patchlevel 3) and above
File:DCF11gp.png
Output DCF11gp.png
File:DCF13gp.png
Output DCF13gp.png
File:DCF15gp.png
Output DCF15gp.png
plotdcf.gp
 ## plotdcf.gp 1/11/17 aev## Plotting a Dragon curve fractal to the png-file. ## Note: assign variables: ord (order), clr (color), filename and ttl (before using load command).## ord (order)  # a.k.a. level - defines size of fractal (also number of mini-curves).resetset style arrow 1 nohead linewidth 1 lc rgb @clrset term png size 1024,1024ofn=filename.ord."gp.png"  # Output file nameset output ofnttl="Dragon curve fractal: order ".ordset title ttl font "Arial:Bold,12"unset border; unset xtics; unset ytics; unset key;set xrange [0:1.0]; set yrange [0:1.0];dragon(n, x, y, dx, dy) = n >= ord ?  \  sprintf("set arrow from %f,%f to %f,%f as 1;", x, y, x + dx, y + dy) : \  dragon(n + 1, x, y, (dx - dy) / 2, (dy + dx) / 2) . \  dragon(n + 1, x + dx, y + dy, - (dx + dy) / 2, (dx - dy) / 2);eval(dragon(0, 0.2, 0.4, 0.7, 0.0))plot -100set output 
Plotting 3 Dragon curve fractals
 ## pDCF.gp 1/11/17 aev## Plotting 3 Dragon curve fractals.## Note: assign variables: ord (order), clr (color), filename and ttl (before using load command).## ord (order)  # a.k.a. level - defines size of fractal (also number of dots).#cd 'C:\gnupData' ##DCF11ord=11; clr = '"red"';filename = "DCF"; ttl = "Dragon curve fractal, order ".ord;load "plotdcf.gp" ##DCF13ord=13; clr = '"brown"';filename = "DCF"; ttl = "Dragon curve fractal, order ".ord;load "plotdcf.gp" ##DCF15ord=15; clr = '"navy"';filename = "DCF"; ttl = "Dragon curve fractal, order ".ord;load "plotdcf.gp" 
Output:
1. All pDCF.gp file commands.
2. 3 plotted png-files: DCF11gp, DCF13gp and DCF15gp


## Gri

Recursively by a dragon curve comprising two smaller dragons drawn towards a midpoint.

Draw Dragon [ from .x1. .y1. to .x2. .y2. [level .level.] ]'Draw a dragon curve going from .x1. .y1. to .x2. .y2. with recursiondepth .level. The total number of line segments for the recursion is 2^level.level=0 is a straight line from x1,y1 to x2,y2. The default for x1,y1 and x2,y2 is to draw horizontally from 0,0to 1,0.{    new .x1. .y1. .x2. .y2. .level.    .x1. = \.word3.    .y1. = \.word4.    .x2. = \.word6.    .y2. = \.word7.    .level. = \.word9.     if {rpn \.words. 5 >=}        .x2. = 1        .y2. = 0    end if    if {rpn \.words. 7 >=}        .level. = 6    end if     if {rpn 0 .level. <=}        draw line from .x1. .y1. to .x2. .y2.    else        .level. = {rpn .level. 1 -}         # xmid,ymid is half way between x1,y1 and x2,y2 and up at        # right angles away.        #        #            xmid,ymid             xmid = (x1+x2 + y2-y1)/2        #            ^       ^             ymid = (x1-x2 + y1+y2)/2        #           /    .    \        #          /     .     \        #     x1,y1 ........... x2,y2        #        new .xmid. .ymid.        .xmid. = {rpn .x1. .x2. + .y2. .y1. - + 2 /}        .ymid. = {rpn .x1. .x2. - .y1. .y2. + + 2 /}         # The recursion is a level-1 dragon from x1,y1 to the midpoint        # and the same from x2,y2 to the midpoint (the latter        # effectively being a revered dragon.)        #        Draw Dragon from .x1. .y1. to .xmid. .ymid. level .level.        Draw Dragon from .x2. .y2. to .xmid. .ymid. level .level.         delete .xmid. .ymid.    end if     delete .x1. .y1. .x2. .y2. .level.} # Dragon curve from 0,0 to 1,0 extends out by 1/3 at the ends, so# extents -0.5 to +1.5 for a bit of margin.  The Y extent is the same# size 2 to make the graph square.set x axis -0.5 1.5   .25set y axis -1 1 .25 Draw Dragon

## Go

Output png

Version using standard image libriary is an adaptation of the version below using the Bitmap task. The only major change is that line drawing code was needed. See comments in code.

package main import (    "fmt"    "image"    "image/color"    "image/draw"    "image/png"    "math"    "os") // separation of the the two endpoints// make this a power of 2 for prettiest outputconst sep = 512// depth of recursion.  adjust as desired for different visual effects.const depth = 14 var s = math.Sqrt2 / 2var sin = []float64{0, s, 1, s, 0, -s, -1, -s}var cos = []float64{1, s, 0, -s, -1, -s, 0, s}var p = color.NRGBA{64, 192, 96, 255}var b *image.NRGBA func main() {    width := sep * 11 / 6    height := sep * 4 / 3    bounds := image.Rect(0, 0, width, height)    b = image.NewNRGBA(bounds)    draw.Draw(b, bounds, image.NewUniform(color.White), image.ZP, draw.Src)    dragon(14, 0, 1, sep, sep/2, sep*5/6)    f, err := os.Create("dragon.png")    if err != nil {        fmt.Println(err)        return    }    if err = png.Encode(f, b); err != nil {        fmt.Println(err)    }    if err = f.Close(); err != nil {        fmt.Println(err)    }} func dragon(n, a, t int, d, x, y float64) {    if n <= 1 {        // Go packages used here do not have line drawing functions        // so we implement a very simple line drawing algorithm here.        // We take advantage of knowledge that we are always drawing        // 45 degree diagonal lines.        x1 := int(x + .5)        y1 := int(y + .5)        x2 := int(x + d*cos[a] + .5)        y2 := int(y + d*sin[a] + .5)        xInc := 1        if x1 > x2 {            xInc = -1        }        yInc := 1        if y1 > y2 {            yInc = -1        }        for x, y := x1, y1; ; x, y = x+xInc, y+yInc {            b.Set(x, y, p)            if x == x2 {                break            }        }        return    }    d *= s    a1 := (a - t) & 7    a2 := (a + t) & 7    dragon(n-1, a1, 1, d, x, y)    dragon(n-1, a2, -1, d, x+d*cos[a1], y+d*sin[a1])}

Original version written to Bitmap task:

package main // Files required to build supporting package raster are found in:// * Bitmap// * Write a PPM file import (    "math"    "raster") // separation of the the two endpoints// make this a power of 2 for prettiest outputconst sep = 512// depth of recursion.  adjust as desired for different visual effects.const depth = 14 var s = math.Sqrt2 / 2var sin = []float64{0, s, 1, s, 0, -s, -1, -s}var cos = []float64{1, s, 0, -s, -1, -s, 0, s}var p = raster.Pixel{64, 192, 96}var b *raster.Bitmap func main() {    width := sep * 11 / 6    height := sep * 4 / 3    b = raster.NewBitmap(width, height)    b.Fill(raster.Pixel{255, 255, 255})    dragon(14, 0, 1, sep, sep/2, sep*5/6)    b.WritePpmFile("dragon.ppm")} func dragon(n, a, t int, d, x, y float64) {    if n <= 1 {        b.Line(int(x+.5), int(y+.5), int(x+d*cos[a]+.5), int(y+d*sin[a]+.5), p)        return    }    d *= s    a1 := (a - t) & 7    a2 := (a + t) & 7    dragon(n-1, a1, 1, d, x, y)    dragon(n-1, a2, -1, d, x+d*cos[a1], y+d*sin[a1])}

import Data.Listimport Graphics.Gnuplot.Simple -- diamonds-- pl = [[0,1],[1,0]] pl = [[0,0],[0,1]]r_90 = [[0,1],[-1,0]] ip :: [Int] -> [Int] -> Intip xs = sum . zipWith (*) xsmatmul xss yss = map (\xs -> map (ip xs ). transpose $yss) xss vmoot xs = (xs++).map (zipWith (+) lxs). flip matmul r_90. map (flip (zipWith (-)) lxs) .reverse . init$ xs   where lxs = last xs dragoncurve = iterate vmoot pl

For plotting I use the gnuplot interface module from hackageDB

Use:

plotPath [] . map (\[x,y] -> (x,y)) $dragoncurve!!13  String rewrite, and outputs a postscript: x 0 = ""x n = (x$n-1)++" +"++(y$n-1)++" f +"y 0 = ""y n = " - f"++(x$n-1)++" -"++(y$n-1) dragon n = concat ["0 setlinewidth 300 400 moveto", "/f{2 0 rlineto}def/+{90 rotate}def/-{-90 rotate}def\n", "f", x n, " stroke showpage"] main = putStrLn$ dragon 14

## HicEst

A straightforward approach, since HicEst does not know recursion (rarely needed in daily work)

    CHARACTER dragon  1  DLG(NameEdit=orders,DNum,  Button='&OK', TItle=dragon) ! input orders    WINDOW(WINdowhandle=wh, Height=1, X=1, TItle='Dragon curves up to order '//orders)     IF( LEN(dragon) < 2^orders) ALLOCATE(dragon, 2^orders)     AXIS(WINdowhandle=wh, Xaxis=2048, Yaxis=2048) ! 2048: black, linear, noGrid, noScales    dragon = ' '    NorthEastSouthWest = 0    x = 0    y = 1    LINE(PenUp, Color=1, x=0, y=0, x=x, y=y)    last = 1     DO order = 1, orders       changeRtoL = LEN_TRIM(dragon) + 1 + (LEN_TRIM(dragon) + 1)/2       dragon = TRIM(dragon) // 'R' // TRIM(dragon)       IF(changeRtoL > 2) dragon(changeRtoL) = 'L'        DO last = last, LEN_TRIM(dragon)          NorthEastSouthWest = MOD( NorthEastSouthWest-2*(dragon(last)=='L')+5, 4 )          x = x + (NorthEastSouthWest==1) - (NorthEastSouthWest==3)          y = y + (NorthEastSouthWest==0) - (NorthEastSouthWest==2)          LINE(Color=order, X=x, Y=y)       ENDDO    ENDDO    GOTO 1 ! this is to stimulate a discussion  END

## Icon and Unicon

The following implements a Heighway Dragon using the Lindenmayer system. It's based on the linden program in the Icon Programming Library.

link linddraw,wopen procedure main() gener   := 12                 # generations w := h := 800                 # window size rewrite := table()            # L rewrite rules rewrite["X"] := "X+YF+" rewrite["Y"] := "-FX-Y" every (C := '') ++:= !!rewrite every /rewrite[c := !C] := c  # map all rule characters  WOpen("size=" || w || "," || h, "dx=" || (w / 2),  "dy=" || (h / 2)) | stop("*** cannot open window") WAttrib("fg=blue")  linddraw(0, 0, "FX", rewrite, 5, 90.0, gener, 0)  #        x,y, axiom, rules, length, angle, generations, delay    WriteImage("dragon-unicon" || ".gif")   # save the image WDone()end

## J

require 'plot'start=: 0 0,: 1 0step=: ],{: +"1 (0 _1,: 1 0) +/ .*~ |[email protected]}: -"1 {:plot <"1 |: step^:13 start

In English: Start with a line segment. For each step of iteration, retrace that geometry backwards, but oriented 90 degrees about its original end point. To show the curve you need to pick some arbitrary number of iterations.

Any line segment is suitable for start. (For example, -start+123 works just fine though of course the resulting orientation and coordinates for the curve will be different from those obtained using start for the line segment.)

For a more colorful display, with a different color for the geometry introduced at each iteration, replace that last line of code with:

([:pd[:<"1|:)every'reset';|.'show';step&.>^:(i.17)<start

The curve can also be represented as a limiting set of the iterated function system

${\displaystyle f_{1}(z)={\frac {(1+i)z}{2}}}$
${\displaystyle f_{2}(z)=1-{\frac {(1-i)z}{2}}}$

Giving the code

require 'plot'f1=.*&(-:1j1)f2=.[: -. *&(-:1j_1)plot (f1,}[email protected]|[email protected])^:12 ]0 1

Where both functions are applied successively to starting complex values of 0 and 1. Note the formatting of f2 as }[email protected]|[email protected] . This allows the plotted path to go in the right order and removes redundant points, paralleling similar operations in the previous solution.

## Java

import java.awt.Color;import java.awt.Graphics;import java.util.*;import javax.swing.JFrame; public class DragonCurve extends JFrame {     private List<Integer> turns;    private double startingAngle, side;     public DragonCurve(int iter) {        super("Dragon Curve");        setBounds(100, 100, 800, 600);        setDefaultCloseOperation(EXIT_ON_CLOSE);        turns = getSequence(iter);        startingAngle = -iter * (Math.PI / 4);        side = 400 / Math.pow(2, iter / 2.);    }     public List<Integer> getSequence(int iterations) {        List<Integer> turnSequence = new ArrayList<Integer>();        for (int i = 0; i < iterations; i++) {            List<Integer> copy = new ArrayList<Integer>(turnSequence);            Collections.reverse(copy);            turnSequence.add(1);            for (Integer turn : copy) {                turnSequence.add(-turn);            }        }        return turnSequence;    }     @Override    public void paint(Graphics g) {        g.setColor(Color.BLACK);        double angle = startingAngle;        int x1 = 230, y1 = 350;        int x2 = x1 + (int) (Math.cos(angle) * side);        int y2 = y1 + (int) (Math.sin(angle) * side);        g.drawLine(x1, y1, x2, y2);        x1 = x2;        y1 = y2;        for (Integer turn : turns) {            angle += turn * (Math.PI / 2);            x2 = x1 + (int) (Math.cos(angle) * side);            y2 = y1 + (int) (Math.sin(angle) * side);            g.drawLine(x1, y1, x2, y2);            x1 = x2;            y1 = y2;        }    }     public static void main(String[] args) {        new DragonCurve(14).setVisible(true);    }}

## JavaScript

### Version #1.

Works with: Chrome 8.0

I'm sure this can be simplified further, but I have this working here!

Though there is an impressive SVG example further below, this uses JavaScript to recurse through the expansion and simply displays each line with SVG. It is invoked as a method DRAGON.fractal(...) as described.

var DRAGON = (function () {   // MATRIX MATH   // -----------    var matrix = {      mult: function ( m, v ) {         return [ m[0][0] * v[0] + m[0][1] * v[1],                  m[1][0] * v[0] + m[1][1] * v[1] ];      },       minus: function ( a, b ) {         return [ a[0]-b[0], a[1]-b[1] ];      },       plus: function ( a, b ) {         return [ a[0]+b[0], a[1]+b[1] ];      }   };     // SVG STUFF   // ---------    // Turn a pair of points into an SVG path like "M1 1L2 2".   var toSVGpath = function (a, b) {  // type system fail      return "M" + a[0] + " " + a[1] + "L" + b[0] + " " + b[1];   };     // DRAGON MAKING   // -------------    // Make a dragon with a better fractal algorithm   var fractalMakeDragon = function (svgid, ptA, ptC, state, lr, interval) {       // make a new <path>      var path = document.createElementNS('http://www.w3.org/2000/svg', 'path');      path.setAttribute( "class",  "dragon");       path.setAttribute( "d", toSVGpath(ptA, ptC) );       // append the new path to the existing <svg>      var svg = document.getElementById(svgid); // call could be eliminated      svg.appendChild(path);       // if we have more iterations to go...      if (state > 1) {          // make a new point, either to the left or right         var growNewPoint = function (ptA, ptC, lr) {            var left  = [[ 1/2,-1/2 ],                          [ 1/2, 1/2 ]];              var right = [[ 1/2, 1/2 ],                         [-1/2, 1/2 ]];             return matrix.plus(ptA, matrix.mult( lr ? left : right,                                                  matrix.minus(ptC, ptA) ));         };           var ptB = growNewPoint(ptA, ptC, lr, state);          // then recurse using each new line, one left, one right         var recurse = function () {            // when recursing deeper, delete this svg path            svg.removeChild(path);             // then invoke again for new pair, decrementing the state            fractalMakeDragon(svgid, ptB, ptA, state-1, lr, interval);            fractalMakeDragon(svgid, ptB, ptC, state-1, lr, interval);         };          window.setTimeout(recurse, interval);      }   };     // Export these functions   // ----------------------   return {      fractal: fractalMakeDragon       // ARGUMENTS      // ---------      //    svgid    id of <svg> element      //    ptA      first point [x,y] (from top left)      //    ptC      second point [x,y]      //    state    number indicating how many steps to recurse      //    lr       true/false to make new point on left or right       // CONFIG      // ------      // CSS rules should be made for the following      //    svg#fractal      //    svg path.dragon   }; }());

My current demo page includes the following to invoke this:

...<script src='./dragon.js'></script>...<div>   <svg xmlns='http://www.w3.org/2000/svg' id='fractal'></svg> </div><script>   DRAGON.fractal('fractal', [100,300], [500,300], 15, false, 700);</script>...

### Version #2.

Works with: Chrome
File:DC11.png
Output DC11.png
File:DC19.png
Output DC19.png
File:DC25.png
Output DC25.png
 <!-- DragonCurve.html --><html><head><script type='text/javascript'>function pDragon(cId) {  // Plotting Dragon curves. 2/25/17 aev  var n=document.getElementById('ord').value;  var sc=document.getElementById('sci').value;  var hsh=document.getElementById('hshi').value;  var vsh=document.getElementById('vshi').value;  var clr=document.getElementById('cli').value;  var c=c1=c2=c2x=c2y=x=y=0, d=1, n=1<<n;  var cvs=document.getElementById(cId);  var ctx=cvs.getContext("2d");  hsh=Number(hsh); vsh=Number(vsh);  x=y=cvs.width/2;  // Cleaning canvas, init plotting  ctx.fillStyle="white"; ctx.fillRect(0,0,cvs.width,cvs.height);  ctx.beginPath();  for(i=0; i<=n;) {    ctx.lineTo((x+hsh)*sc,(y+vsh)*sc);    c1=c&1; c2=c&2;    c2x=1*d; if(c2>0) {c2x=(-1)*d}; c2y=(-1)*c2x;    if(c1>0) {y+=c2y} else {x+=c2x}    i++; c+=i/(i&-i);  }  ctx.strokeStyle = clr;  ctx.stroke();}</script></head><body><p><b>Please input order, scale, x-shift, y-shift, color:</></p><input id=ord value=11 type="number" min="7" max="25" size="2"><input id=sci value=7.0 type="number" min="0.001" max="10" size="5"><input id=hshi value=-265 type="number" min="-50000" max="50000" size="6"><input id=vshi value=-260 type="number" min="-50000" max="50000" size="6"><input id=cli value="red" type="text" size="14"><button onclick="pDragon('canvId')">Plot it!</button><h3>Dragon curve</h3><canvas id="canvId" width=640 height=640 style="border: 2px inset;"></canvas></body></html>

Testing cases:

Input parameters:

ord scale x-shift y-shift color   [File name to save]
-------------------------------------------
11  7.    -265   -260   red       DC11.png
15  2.    -205   -230   brown     DC15.png
17  1.    -135    70    green     DC17.png
19  0.6    380    440   navy      DC19.png
21  0.22   1600   800   blue      DC21.png
23  0.15   1100   800   violet    DC23.png
25  0.07   2100   5400  darkgreen DC25.png
===========================================

Output:
Page with different plotted Dragon curves. Right-clicking on the canvas you can save each of them
as a png-file.


## jq

Works with: jq version 1.4

The following is based on the JavaScript example, with some variations, notably:

• the last argument of the main function allows CSS style elements to be specified
• the output is a single SVG element that can, for example, be viewed in a web browser such as Chrome, Firefox, or Safari
• only one "path" element is emitted.

The main function is fractalMakeDragon(svgid; ptA; ptC; steps; left; style) where:

     #    svgid    id of <svg> element
#    ptA      first point [x,y] (from top left)
#    ptC      second point [x,y]
#    steps    number indicating how many steps to recurse
#    left     if true, make new point on left; if false, then on right
#    css      a JSON object optionally specifying "stroke" and "stroke-width"

# MATRIX MATH  def mult(m; v):    [ m[0][0] * v[0] + m[0][1] * v[1],      m[1][0] * v[0] + m[1][1] * v[1] ];   def minus(a; b): [ a[0]-b[0], a[1]-b[1] ];   def plus(a; b):  [ a[0]+b[0], a[1]+b[1] ]; # SVG STUFF  # default values of stroke and stroke-width are provided  def style(obj):    { "stroke": "rgb(255, 15, 131)", "stroke-width": "2px" } as $default | ($default + obj) as $s | "<style type='text/css' media='all'> .dragon { stroke:\($s.stroke); stroke-width:\($s["stroke-width"]); } </style>"; def svg(id; width; height): "<svg width='\(width // "100%")' height='\(height // "100%") ' id='\(id)' xmlns='http://www.w3.org/2000/svg'>"; # Turn a pair of points into an SVG path like "M1 1L2 2" (M=move to; L=line to). def toSVGpath(a; b): "M\(a[0]) \(a[1])L\(b[0]) \(b[1])"; # DRAGON MAKING def fractalMakeDragon(svgid; ptA; ptC; steps; left; css): # Make a new point, either to the left or right def growNewPoint(ptA; ptC; left): [[ 1/2,-1/2 ], [ 1/2, 1/2 ]] as$left      | [[ 1/2, 1/2 ], [-1/2, 1/2 ]]  as $right | plus(ptA; mult(if left then$left else $right end; minus(ptC; ptA))); def grow(ptA; ptC; steps; left): # if we have more iterations to go... if steps > 1 then growNewPoint(ptA; ptC; left) as$ptB        # ... then recurse using each new line, one left, one right        | grow($ptB; ptA; steps-1; left), grow($ptB; ptC; steps-1; left)      else        toSVGpath(ptA; ptC)      end;     svg(svgid; "100%"; "100%"),      style(css),      "<path class='dragon' d='",         grow(ptA; ptC; steps; left),      "'/>",    "</svg>";

Example:

# Default values are provided for the last argumentfractalMakeDragon("roar"; [100,300]; [500,300]; 15; false; {})
Output:

The command to generate the SVG and the first few lines of output are as follows:

## M4

This code uses the "predicate" approach. A given x,y position is tested by a predicate as to whether it's on the curve or not and printed as a character or a space accordingly. The output goes row by row and column by column with no image storage or buffering.

# The macros which return a pair of values x,y expand to an unquoted 123,456# which is suitable as arguments to a further macro.  The quoting is slack# because the values are always integers and so won't suffer unwanted macro# expansion. #                0,1                 Vertex and segment x,y numbering.#                 |#                 |                  Segments are numbered as if a#                 |s=0,1             square grid turned anti-clockwise#                 |                  by 45 degrees.#                 |#  -1,0 -------- 0,0 -------- 1,0    vertex_to_seg_east(x,y) returns#        s=-1,1   |   s=0,0          the segment x,y to the East,#                 |                  so vertex_to_seg_east(0,0) is 0,0#                 |#                 |s=-1,0            vertex_to_seg_west(x,y) returns#                 |                  the segment x,y to the West,#                0,-1                so vertex_to_seg_west(0,0) is -1,1#define(vertex_to_seg_east',  eval($1 +$2),     eval($2 -$1)')define(vertex_to_seg_west',  eval($1 +$2 - 1), eval($2 -$1 + 1)')define(vertex_to_seg_south', eval($1 +$2 - 1), eval($2 -$1)') # Some past BSD m4 didn't have "&" operator, so mod2(n) using % instead.# mod2() returns 0,1 even if "%" gives -1 for negative odds.#define(mod2', ifelse(eval($1 % 2),0,0,1)') # seg_to_even(x,y) returns x,y moved to an "even" position by subtracting an# offset in a way which suits the segment predicate test.## seg_offset_y(x,y) is a repeating pattern## | 1,1,0,0# | 1,1,0,0# | 0,0,1,1# | 0,0,1,1# +---------## seg_offset_x(x,y) is the same but offset by 1 in x,y## | 0,1,1,0# | 1,0,0,1# | 1,0,0,1# | 0,1,1,0# +---------## Incidentally these offset values also give n which is the segment number# along the curve. "x_offset XOR y_offset" is 0,1 and is a bit of n from# low to high.#define(seg_offset_y', mod2(eval(($1 >> 1) + ($2 >> 1)))')define(seg_offset_x', seg_offset_y(eval($1+1), eval($2+1))')define(seg_to_even', eval($1 - seg_offset_x($1,$2)),                       eval($2 - seg_offset_y($1,$2))'); # xy_div_iplus1(x,y) returns x,y divided by complex number i+1.# So (x+i*y)/(i+1) which means newx = (x+y)/2, newy = (y-x)/2.# Must have x,y "even", meaning x+y even, so newx and newy are integers.#define(xy_div_iplus1', eval(($1 + $2)/2), eval(($2 - $1)/2)') # seg_is_final(x,y) returns 1 if x,y is one of the final four points.# On these four points xy_div_iplus1(seg_to_even(x,y)) returns x,y# unchanged, so the seg_pred() recursion does not reduce any further.## .. | ..# final | final y=+1# final | final y=0# -------+--------# .. | ..# x=-1 x=0#define(seg_is_final', eval(($1==-1 || $1==0) && ($2==1 || $2==0))') # seg_pred(x,y) returns 1 if segment x,y is on the dragon curve.# If the final point reached is 0,0 then the original x,y was on the curve.# (If a different final point then x,y was one of four rotated copies of the# curve.)#define(seg_pred', ifelse(seg_is_final($1,$2), 1, eval($1==0 && $2==0)', seg_pred(xy_div_iplus1(seg_to_even($1,$2)))')') # vertex_pred(x,y) returns 1 if point x,y is on the dragon curve.# The curve always turns left or right at a vertex, it never crosses itself,# so if a vertex is visited then either the segment to the east or to the# west must have been traversed. Prefer ifelse() for the two checks since# eval() || operator is not a short-circuit.#define(vertex_pred', ifelse(seg_pred(vertex_to_seg_east($1,$2)),1,1, seg_pred(vertex_to_seg_west($1,$2))')') # forloop(varname, start,end, body)# Expand body with varname successively define()ed to integers "start" to# "end" inclusive. "start" to "end" can go either increasing or decreasing.#define(forloop', define($1',$2)$4'dnlifelse($2,$3,,forloop($1',eval($2 + 2*($2 <$3) - 1), $3, $4')')') #---------------------------------------------------------------------------- # dragon01(xmin,xmax, ymin,ymax) prints an array of 0s and 1s which are the# vertex_pred() values.  y' runs from ymax down to ymin so that y# coordinate increases up the screen.#define(dragon01',forloop(y',$4,$3, forloop(x',$1,$2, vertex_pred(x,y)')')') # dragon_ascii(xmin,xmax, ymin,ymax) prints an ascii art dragon curve.# Each y value results in two output lines.  The first has "+" vertices and# "--" horizontals.  The second has "|" verticals.#define(dragon_ascii',forloop(y',$4,$3,forloop(x',$1,$2,ifelse(vertex_pred(x,y),1, +',  ')dnlifelse(seg_pred(vertex_to_seg_east(x,y)), 1, --',   ')')forloop(x',$1,$2,ifelse(seg_pred(vertex_to_seg_south(x,y)), 1, |  ',    ')')')') #--------------------------------------------------------------------------divert'dnl # 0s and 1s directly from vertex_pred().#dragon01(-7,23,      dnl X range         -11,10)     dnl Y range # ASCII art lines.#dragon_ascii(-6,5,      dnl X range             -10,2)     dnl Y range
Output
# 0s and 1s directly from vertex_pred().
#
0000000000000000011111110000000
0000000000000011011111111000000
0000000000000111011111111000000
0000000000000111111111100000000
0000000000000111111111111111000
0000000000000111111111111111100
0000000000000001111111111111100
0000000000000001111111111110000
0000111100000000011111111111000
0000111110000011011110001111100
0011110110000111011110111111100
0011110000000111111000111110000
0001110000000111111100011110000
0000111100110111111110000000000
0011111101110111111110000000000
0011111111111111111000000000000
0001111111111111111100000000000
0000000011111000111110000000000
0000001111111011111110000000000
0000001111100011111000000000000
0000000111100001111000000000000
0000000000000000000000000000000

# ASCII art lines.
#
+--+  +--+
|  |  |  |
+--+--+  +--+
|        |
+--+  +--+     +--+
|  |  |
+--+--+--+
|  |  |
+--+--+
|
+--+  +--+        +--+
|  |  |        |  |
+--+  +--+--+--+     +--+--+
|  |  |  |  |        |  |
+--+--+--+--+--+  +--+--+--+  +--
|  |  |  |  |  |  |  |  |  |
+--+  +--+  +--+--+--+--+--+
|  |  |  |
+--+--+--+--+
|  |  |  |
+--+  +--+--+  +--+
|  |  |  |
+--+--+--+--+
|  |  |  |
+--+  +--+

## Mathematica / Wolfram Language

Two functions: one that makes 2 lines from 1 line. And another that applies this function to all existing lines:

FoldOutLine[{a_,b_}]:={{a,#},{b,#}}&[a+0.5(b-a)+{{0.,0.5},{-0.5,0.}}.(b-a)]NextStep[in_]:=Flatten[FoldOutLine/@in,1]lines={{{0.,0.},{1.,0.}}};Graphics[Line/@Nest[NextStep,lines,11]]

## Metafont

Metafont is a language to create fonts; since fonts normally are not too big, Metafont has hard encoded limits which makes it difficult to produce large images. This is one of the reasons why Metapost came into being.

The following code produces a single character font, 25 points wide and tall (0 points in depth), and store it in the position where one could expect to find the character D.

mode_setup;dragoniter := 8;beginchar("D", 25pt#, 25pt#, 0pt#);  pickup pencircle scaled .5pt;  x1 = 0; x2 = w; y1 = y2 = .5h;  mstep := .5; sg := -1;  for i = 1 upto dragoniter:    for v = 1 step mstep until (2-mstep):      if unknown z[v+mstep]:	pair t;	t := .7071[ z[v], z[v+2mstep] ];	z[v+mstep] = t rotatedaround(z[v], 45sg);	sg := -1*sg;      fi    endfor    mstep := mstep/2;   endfor  draw for v:=1 step 2mstep until (2-2mstep): z[v] -- endfor z[2];endchar;end

The resulting character, magnified by 2, looks like:

## OCaml

Library: Tk

Example solution, using an OCaml class and displaying the result in a Tk canvas, mostly inspired by the Tcl solution.

(* This constant does not seem to be defined anywhere in the standard modules *)let pi = acos (-1.0); (*** CLASS dragon_curve_computer:** ----------------------------** Computes the coordinates for the line drawing the curve.** - initial_x initial_y: coordinates for starting point for curve** - total_length: total length for the curve** - total_splits: total number of splits to perform*)class dragon_curve_computer initial_x initial_y total_length total_splits =  object(self)    val mutable current_x = (float_of_int initial_x)  (* current x coordinate in curve *)    val mutable current_y = (float_of_int initial_y)  (* current y coordinate in curve *)    val mutable current_angle = 0.0                   (* current angle *)     (*    ** METHOD compute_coords:    ** ----------------------    ** Actually computes the coordinates in the line for the curve    ** - length: length for current iteration    ** - nb_splits: number of splits to perform for current iteration    ** - direction: direction for current line (-1.0 or 1.0)    ** Returns: the list of coordinates for the line in this iteration    *)    method compute_coords length nb_splits direction =      (* If all splits have been done *)      if nb_splits = 0      then        begin          (* Draw line segment, updating current coordinates *)          current_x <- current_x +. length *. cos current_angle;          current_y <- current_y +. length *. sin current_angle;          [(int_of_float current_x, int_of_float current_y)]        end      (* If there are still splits to perform *)      else        begin          (* Compute length for next iteration *)          let sub_length = length /. sqrt 2.0 in          (* Turn 45 degrees to left or right depending on current direction and draw part              of curve in this direction *)          current_angle <- current_angle +. direction *. pi /. 4.0;          let coords1 = self#compute_coords sub_length (nb_splits - 1) 1.0 in          (* Turn 90 degrees in the other direction and draw part of curve in that direction *)          current_angle <- current_angle -. direction *. pi /. 2.0;          let coords2 = self#compute_coords sub_length (nb_splits - 1) (-1.0) in          (* Turn back 45 degrees to set head in the initial direction again *)          current_angle <- current_angle +. direction *. pi /. 4.0;          (* Concatenate both sub-curves to get the full curve for this iteration *)          coords1 @ coords2        end     (*    ** METHOD get_coords:    ** ------------------    ** Returns the coordinates for the curve with the parameters set in the object initializer    *)    method get_coords = self#compute_coords total_length total_splits 1.0  end;;  (*** MAIN PROGRAM:** =============*)let () =  (* Curve is displayed in a Tk canvas *)  let top=Tk.openTk() in  let c = Canvas.create ~width:400 ~height:400 top in  Tk.pack [c];  (* Create instance computing the curve coordinates *)  let dcc = new dragon_curve_computer 100 200 200.0 16 in  (* Create line with these coordinates in canvas *)  ignore (Canvas.create_line ~xys: dcc#get_coords c);  Tk.mainLoop ();;;

### A functional version

Here is another OCaml solution, in a functional rather than OO style:

let zig (x1,y1) (x2,y2) = (x1+x2+y1-y2)/2, (x2-x1+y1+y2)/2let zag (x1,y1) (x2,y2) = (x1+x2-y1+y2)/2, (x1-x2+y1+y2)/2 let rec dragon p1 p2 p3 n =   if n = 0 then [p1;p2] else   (dragon p1 (zig p1 p2) p2 (n-1)) @ (dragon p2 (zag p2 p3) p3 (n-1)) let _ =   let top = Tk.openTk() in   let c = Canvas.create ~width:430 ~height:300 top in   Tk.pack [c];   let p1, p2 = (100, 100), (356,100) in   let points = dragon p1 (zig p1 p2) p2 15 in   ignore (Canvas.create_line ~xys: points c);   Tk.mainLoop ()

producing:

Run an example with:

ocaml -I +labltk labltk.cma dragon.ml


Using the two sub-curves inward approach. The sub-curves are rotated and shifted explicitly. That could be combined into a multmatrix() each if desired. Lines segments are drawn as elongated cuboids.

level = 8;linewidth = .1;  // fraction of segment lengthsqrt2 = pow(2, .5); // Draw a dragon curve "level" going from [0,0] to [1,0]module dragon(level) {    if (level <= 0) {        translate([.5,0]) cube([1+linewidth,linewidth,linewidth],center=true);    } else {        rotate(-45) scale(1/sqrt2) dragon(level-1);        translate([1,0]) rotate(-135) scale(1/sqrt2) dragon(level-1);    }} scale(40) {  // scale to nicely visible in the default GUI    sphere(1.5*linewidth / pow(2,level/2));  // mark the start of the curve    dragon(level);}

## PARI/GP

### Version #1.

Using the "high level" plothraw with real and imaginary parts of vertex points as X and Y coordinates. Change plothraw() to psplothraw() to write a PostScript file "pari.ps" instead of drawing on-screen.

level = 13p = [0, 1];  \\ complex number points, initially 0 to 1 \\ "unfold" at the current endpoint p[#p].\\ p[^-1] so as not to duplicate that endpoint.\\ \\           *  end\\      -->  |\\     /     |\\           v\\  *------->*\\ 0,0       p[#p]\\for(i=1,level, my(end = (1+I)*p[#p]); \               p = concat(p, apply(z->(end - I*z), Vecrev(p[^-1])))) plothraw(apply(real,p),apply(imag,p), 1); \\ flag=1 join points

### Version #2.

Using the "low level" plotting functions to draw to a GUI window (X etc).

len=256; bit_above_low_1(n) = bittest(n, valuation(n,2)+1); plotinit(0);plotscale(0, -32,32, 32,-32); \\ Y increasing up the screenplotmove(0, 0,0);plotstring(0, "start", 8+32); \\ flags 8=top + 32=gap dx=1;dy=0;turn_right()= [dx,dy]=[-dy,dx];turn_left() = [dx,dy]=[dy,-dx]; for(i=1,len, plotrline(0,dx,dy); \             if(bit_above_low_1(i), turn_right(), turn_left()));plotdraw([0,100,100]);

### Version #3.

Output Dragon13.png
Output Dragon17.png
Output Dragon21.png

This is actualy Version #1 upgraded to the reusable function.

Works with: PARI/GP version 2.7.4 and above
 \\ Dragon curve\\ 4/8/16 aevDragon(level)={my(p=[0,1],end);print(" *** Dragon curve, level ",level);for(i=1,level, end=(1+I)*p[#p];    p=concat(p,apply(z->(end-I*z),Vecrev(p[^-1]))) );plothraw(apply(real,p),apply(imag,p), 1);} {\\ Executing/Testing: Dragon(13); \\ Dragon13.png Dragon(17); \\ Dragon17.png Dragon(21); \\ Dragon21.png Dragon(23); \\ No result}
Output:
 *** Dragon curve, level 13
***   last result computed in 282 ms.

*** Dragon curve, level 17
***   last result computed in 453 ms.

*** Dragon curve, level 21
***   last result computed in 7,266 ms.

*** Dragon curve, level 23
*** concat: the PARI stack overflows !
***   last result computed in 0 ms.



## Pascal

using Compas (Pascal with Logo-expansion):

procedure dcr(step,dir:integer;length:real); begin;  step:=step -1;  length:= length/sqrt(2);  if dir > 0 then   begin     if step > 0 then     begin       turnright(45);       dcr(step,1,length);       turnleft(90);       dcr(step,0,length);       turnright(45);     end     else     begin       turnright(45);       forward(length);       turnleft(90);       forward(length);       turnright(45);     end;   end  else   begin     if step > 0 then     begin       turnleft(45);       dcr(step,1,length);       turnright(90);       dcr(step,0,length);       turnleft(45);     end     else     begin       turnleft(45);       forward(length);       turnright(90);       forward(length);       turnleft(45);     end;   end;end;

main program:

begin init; penup; back(100); pendown; dcr(step,direction,length); close;end.

## Perl

As in the Perl 6 solution, we'll use a Lindenmayer system and draw the dragon in SVG.

use SVG;use List::Util qw(max min); use constant pi => 2 * atan2(1, 0); # Compute the curve with a Lindemayer-systemmy %rules = (    X => 'X+YF+',    Y => '-FX-Y');my $dragon = 'FX';$dragon =~ s/([XY])/$rules{$1}/eg for 1..10; # Draw the curve in SVG($x,$y) = (0, 0);$theta = 0;$r       = 6; for (split //, $dragon) { if (/F/) { push @X, sprintf "%.0f",$x;        push @Y, sprintf "%.0f", $y;$x += $r * cos($theta);        $y +=$r * sin($theta); } elsif (/\+/) {$theta += pi/2; }    elsif (/\-/) { $theta -= pi/2; }}$xrng =  max(@X) - min(@X);$yrng = max(@Y) - min(@Y);$xt   = -min(@X)+10;$yt = -min(@Y)+10;$svg = SVG->new(width=>$xrng+20, height=>$yrng+20);$points =$svg->get_path(x=>\@X, y=>\@Y, -type=>'polyline');$svg->rect(width=>"100%", height=>"100%", style=>{'fill'=>'black'});$svg->polyline(%$points, style=>{'stroke'=>'orange', 'stroke-width'=>1}, transform=>"translate($xt,$yt)"); open$fh, '>', 'dragon_curve.svg';print $fh$svg->xmlify(-namespace=>'svg');close $fh; Dragon curve (offsite image) ## Perl 6 We'll use a L-System role, and draw the dragon in SVG. use SVG; role Lindenmayer { has %.rules; method succ { self.comb.map( { %!rules{$^c} // $c } ).join but Lindenmayer(%!rules) }} my$dragon = "FX" but Lindenmayer( { X => 'X+YF+', Y => '-FX-Y' } ); $dragon++ xx ^15; my @points = 215, 350; for$dragon.comb {    state ($x,$y) = @points[0,1];    state $d = 2 + 0i; if /'F'/ { @points.append: ($x += $d.re).round(.1), ($y += $d.im).round(.1) } elsif /< + - >/ {$d *= "{_}1i" }} say SVG.serialize( svg => [ :600width, :450height, :style<stroke:rgb(0,0,255)>, :rect[:width<100%>, :height<100%>, :fill<white>], :polyline[ :points(@points.join: ','), :fill<white> ], ],); ## Phix Library: pGUI Changing the colour and depth give some mildly interesting results. ---- demo\rosetta\DragonCurve.exw--include pGUI.e Ihandle dlg, canvascdCanvas cddbuffer, cdcanvas integer colour = 0 procedure Dragon(integer depth, atom x1, y1, x2, y2) depth -= 1 if depth<=0 then cdCanvasSetForeground(cddbuffer, colour) cdCanvasLine(cddbuffer, x1, y1, x2, y2) -- (some interesting colour patterns emerge) colour += 2-- colour += 2000-- colour += #100 else atom dx = x2-x1, dy = y2-y1, nx = x1+(dx-dy)/2, ny = y1+(dx+dy)/2 Dragon(depth,x1,y1,nx,ny) Dragon(depth,x2,y2,nx,ny) end ifend procedure function redraw_cb(Ihandle /*ih*/, integer /*posx*/, integer /*posy*/) cdCanvasActivate(cddbuffer) cdCanvasClear(cddbuffer) -- (note: depths over 21 take a long time to draw, -- depths <= 16 look a little washed out) Dragon(17,100,100,100+256,100) cdCanvasFlush(cddbuffer) return IUP_DEFAULTend function function map_cb(Ihandle ih) cdcanvas = cdCreateCanvas(CD_IUP, ih) cddbuffer = cdCreateCanvas(CD_DBUFFER, cdcanvas) cdCanvasSetBackground(cddbuffer, CD_PARCHMENT) return IUP_DEFAULTend function function esc_close(Ihandle /*ih*/, atom c) if c=K_ESC then return IUP_CLOSE end if return IUP_CONTINUEend function procedure main() IupOpen() canvas = IupCanvas(NULL) IupSetAttribute(canvas, "RASTERSIZE", "420x290") IupSetCallback(canvas, "MAP_CB", Icallback("map_cb")) IupSetCallback(canvas, "ACTION", Icallback("redraw_cb")) dlg = IupDialog(canvas,"RESIZE=NO") IupSetAttribute(dlg, "TITLE", "Dragon Curve") IupSetCallback(dlg, "K_ANY", Icallback("esc_close")) IupShow(dlg) IupMainLoop() IupClose()end procedure main() ## PicoLisp Translation of: Forth This uses the 'brez' line drawing function from Bitmap/Bresenham's line algorithm#PicoLisp. # Need some turtle graphics(load "@lib/math.l") (setq *TurtleX 100 # X position *TurtleY 75 # Y position *TurtleA 0.0 ) # Angle (de fd (Img Len) # Forward (let (R (*/ *TurtleA pi 180.0) DX (*/ (cos R) Len 1.0) DY (*/ (sin R) Len 1.0)) (brez Img *TurtleX *TurtleY DX DY) (inc '*TurtleX DX) (inc '*TurtleY DY) ) ) (de rt (A) # Right turn (inc '*TurtleA A) ) (de lt (A) # Left turn (dec '*TurtleA A) ) # Dragon curve stuff(de *DragonStep . 4) (de dragon (Img Depth Dir) (if (=0 Depth) (fd Img *DragonStep) (rt Dir) (dragon Img (dec Depth) 45.0) (lt (* 2 Dir)) (dragon Img (dec Depth) -45.0) (rt Dir) ) ) # Run it(let Img (make (do 200 (link (need 300 0)))) # Create image 300 x 200 (dragon Img 10 45.0) # Build dragon curve (out "img.pbm" # Write to bitmap file (prinl "P1") (prinl 300 " " 200) (mapc prinl Img) ) ) ## PL/I This was written for the Ministry of Works IBM390 system running MVS/XA. Odd results when linking from a library of previously-compiled procedures led to the preference for employing libraries via including source files. That way, all of the prog. would be compiled with the same settings: optimisation, bound checking, etc. and the odd behaviour vanished. As complexity grew, these libraries tended to take advantage of each other, so small ad-hoc progs. still ended up needing many inclusions. GOODIES for example defined INTEGER to be FIXED BINARY(16,0), BOOLEAN as FIXED BIT(1) ALIGNED, etc. and so was nearly always wanted. RUNFILE offered an interface to the special assembler routines (written by the MOW) that enabled run-time file allocation and also helped with error messages. CARDINAL and ORDINAL are for presenting numbers as texts. And PSTUFF supplied my notions of an interface to the local plotting routines that allowed output to an IBM3268 screen or a CalComp pen plotter and a few others. These routines are alas no longer available, but I do have an order 19 Dragoncurve that was plotted on a sheet of 32" by 56" by the Calcomp shortly before it was retired, still in excellent order: the + plotted at the start and the x at the end were perfectly aligned. To the 119 secs of cpu time to generate the plot file (the Calcomp format was used, in units of a thousandth of an inch), a further 350 seconds was needed to present the results to the plotter. The charge rate was a dollar a second... The source file was used to test plotting opportunities, and I have removed the code to draw the likes of a snowflake, pursuit curves, Lissajou curves, and a few others. If the dragon curve order was less than twelve, then all up to that order would be drawn, otherwise only the specified order for the larger jobs. The odd layout (especially of the documentation for DRAGONCURVE) was grist to the "prettyprint" process of PLIST that would list pl/i source files with whole-line comments textflowed into a lineprinter width of 132 columns and end-of-line comments were aligned to the right, away from the source on the left. Each printer line began with the line sequence number, normally in columns 73-80, though they have been removed here. Display screens only had a width of 72 for the source and six for the line sequence: with the ISPF editor, each field control code occupied one space on the display. The method uses a bit string to represent the turn direction, and each "fold" to construct the next dragon curve involved appending an inverted and reversed copy of the current bit string to the end of the current string after a "1" bit representing the fold. That is, source 1 ecruos where "ecruos" is inverted via not - this scheme was described to me by an acquaintance at Auckland University in 1970. The dragon curve was not drawn by straight lines, because that meant that the dragon curve would intersect with itself at many corners. So, instead of showing each bend as two lines at right angles, a quarter-turn of a circle was used with the same orientation. No collisions, and no bewildering areas of simple squares huddled together. There cannot be any intersections, because the original involves a sheet of paper and no matter how folded it never passes through itself. A restriction of the pl/i compiler in the 1980s was that array indices could not exceed 32767, thus the escalation to a two-dimensional array, as in DECLARE FOLD(0:31,0:32767) BOOLEAN; /*Oh for (0:1000000) or so..*/ This made the array indexing rather messy.  * PROCESS GONUMBER, MARGINS(1,72), NOINTERRUPT, MACRO;TEST:PROCEDURE OPTIONS(MAIN); DECLARE SYSIN FILE STREAM INPUT, DRAGON FILE STREAM OUTPUT PRINT, SYSPRINT FILE STREAM OUTPUT PRINT; DECLARE (MIN,MAX,MOD,INDEX,LENGTH,SUBSTR,VERIFY,TRANSLATE) BUILTIN; DECLARE (COMPLEX,SQRT,REAL,IMAG,ATAN,SIN,EXP,COS,ABS) BUILTIN; %INCLUDE PLILIB(GOODIES); %INCLUDE PLILIB(SCAN); %INCLUDE PLILIB(GRAMMAR); %INCLUDE PLILIB(CARDINAL); %INCLUDE PLILIB(ORDINAL); %INCLUDE PLILIB(ANSWAROD); %INCLUDE PLILIB(RUNFILE); %INCLUDE PLILIB(PSTUFF); DECLARE (TWOPI,TORAD) REAL; DECLARE RANGE(4) REAL; DECLARE TRACERANGE BOOLEAN INITIAL(FALSE); DECLARE FRESHRANGE BOOLEAN INITIAL(TRUE); BOUND:PROCEDURE(Z); DECLARE Z COMPLEX; DECLARE (ZX,ZY) REAL; ZX = REAL(Z); ZY = IMAG(Z); IF FRESHRANGE THEN DO; RANGE(1),RANGE(2) = ZX; RANGE(3),RANGE(4) = ZY; END; ELSE DO; RANGE(1) = MIN(RANGE(1),ZX); RANGE(2) = MAX(RANGE(2),ZX); RANGE(3) = MIN(RANGE(3),ZY); RANGE(4) = MAX(RANGE(4),ZY); END; FRESHRANGE = FALSE; END BOUND; PLOTZ:PROCEDURE(Z,PEN); DECLARE Z COMPLEX; DECLARE PEN INTEGER; IF TRACERANGE THEN CALL BOUND(Z); CALL PLOT(REAL(Z),IMAG(Z),PEN); END PLOTZ; %PAGE; DRAGONCURVE:PROCEDURE(ORDER,HOP); /*Folding paper in two...*//*Some statistics on runs with x = 56.25", y = 32.6"&(the calcomp plotter).*//*The actual size of the picture determines the number of steps&to each quarter-turn.*//* n turns x y secs dx dy&*//* 20 1,048,575 -2389:681 -682:1364 180+ 3070 2046&*//* 19 524,287 -1365:681 -340:1364 119 2046 1704&*//* 18 262,143 -341:681 -340:1194 71 1022 1554&*//* 17 131,071 -171:681 -340:682 35 852 1022&*/ DECLARE ORDER BIGINT; /*So how many folds.*/ DECLARE HOP BOOLEAN; DECLARE FOLD(0:31,0:32767) BOOLEAN; /*Oh for (0:1000000) or so..*/ DECLARE (TURN,N,IT,I,I1,I2,J1,J2,L,LL) BIGINT; DECLARE (XMIN,XMAX,YMIN,YMAX,XMID,YMID) REAL; DECLARE (IXMIN,IXMAX,IYMIN,IYMAX) BIGINT; DECLARE (S,H,TORAD) REAL; DECLARE (ZMID,Z,Z2,DZ,ZL) COMPLEX; DECLARE (FULLTURN,ABOUTTURN,QUARTERTURN) INTEGER; DECLARE (WAY,DIRECTION,ND,LD,LD1,LD2) INTEGER; DECLARE LEAF(0:3,0:360) COMPLEX; /*Corner turning.*/ DECLARE SWAPXY BOOLEAN; /*Try to align rectangles.*/ DECLARE (T1,T2) CHARACTER(200) VARYING; IF ¬PLOTCHOICE('') THEN RETURN; /*Ascertain the plot device.*/ N = 0; FOR TURN = 1 TO ORDER; IT = N + 1; I1 = IT/32768; I2 = MOD(IT,32768); FOLD(I1,I2) = TRUE; FOR I = 1 TO N; I1 = (IT + I)/32768; I2 = MOD(IT + I,32768); J1 = (IT - I)/32768; J2 = MOD(IT - I,32768); FOLD(I1,I2) = ¬FOLD(J1,J2); END; N = N*2 + 1; IF HOP & TURN < ORDER THEN GO TO XX; XMIN,XMAX,YMIN,YMAX = 0; Z = 0; /*Start at the origin.*/ DZ = 1; /*Step out unilaterally.*/ FOR I = 1 TO N; Z = Z + DZ; /*Take the step before the kink.*/ I1 = I/32768; I2 = MOD(I,32768); IF FOLD(I1,I2) THEN DZ = DZ*(0 + 1I); ELSE DZ = DZ*(0 - 1I); Z = Z + DZ; /*The step after the kink.*/ XMIN = MIN(XMIN,REAL(Z)); XMAX = MAX(XMAX,REAL(Z)); YMIN = MIN(YMIN,IMAG(Z)); YMAX = MAX(YMAX,IMAG(Z)); END; SWAPXY = ((XMAX - XMIN) >= (YMAX - YMIN)) /*Contemplate */ ¬= (PLOTSTUFF.XSIZE >= PLOTSTUFF.YSIZE); /* rectangularities.*/ IF SWAPXY THEN DO; H = XMIN; XMIN = YMIN; YMIN = -XMAX; XMAX = YMAX; YMAX = -H; END; IXMAX = XMAX; IYMAX = YMAX; IXMIN = XMIN; IYMIN = YMIN; XMID = (XMAX + XMIN)/2; YMID = (YMAX + YMIN)/2; ZMID = COMPLEX(XMID,YMID); XMAX = XMAX - XMID; YMAX = YMAX - YMID; XMIN = XMIN - XMID; YMIN = YMIN - YMID; T1 = 'Order ' || IFMT(TURN) || ' Dragoncurve, ' || SAYNUM(0,N,'turn') || '.'; IF SWAPXY THEN T2 = 'y range ' || IFMT(IYMIN) || ':' || IFMT(IYMAX) || ', x range ' || IFMT(IXMIN) || ':' || IFMT(IXMAX); ELSE T2 = 'x range ' || IFMT(IXMIN) || ':' || IFMT(IXMAX) || ', y range ' || IFMT(IYMIN) || ':' || IFMT(IYMAX); S = MIN(PLOTSTUFF.XSIZE/(XMAX - XMIN), /*Rectangularity */ (PLOTSTUFF.YSIZE - 4*H)/(YMAX - YMIN)); /* matching?*/ H = MIN(PLOTSTUFF.XSIZE,S*(XMAX - XMIN)); /*X-width for text.*/ H = MIN(PLOTCHAR,H/(MAX(LENGTH(T1),LENGTH(T2)) + 6)); IF ¬NEWRANGE(XMIN*S,XMAX*S,YMIN*S-2*H,YMAX*S+2*H) THEN STOP('Urp!'); CALL PLOTTEXT(-LENGTH(T1)*H/2,YMAX*S + 2*PLOTTICK,H,T1,0); CALL PLOTTEXT(-LENGTH(T2)*H/2,YMIN*S - 2*H + 2*PLOTTICK,H,T2,0); QUARTERTURN = MIN(MAX(3,12*SQRT(S)),90); /*Angle refinement.*/ ABOUTTURN = QUARTERTURN*2; FULLTURN = QUARTERTURN*4; /*Ensures divisibility.*/ TORAD = TWOPI/FULLTURN; /*Imagine if FULLTURN was 360.*/ ZL = 1; /*Start with 0 degrees.*/ FOR L = 0 TO 3; /*The four directions.*/ FOR I = 0 TO FULLTURN; /*Fill out the petals in the corner.*/ LEAF(L,I) = ZL + EXP((0 + 1I)*I*TORAD); /*Poke!*/ END; /*Fill out the full circle for each for simplicity.*/ ZL = ZL*(0 + 1I); /*Rotate to the next axis.*/ END; /*Four circles, centred one unit along each axial direction.*/ Z = -ZMID; /*The start point. Was 0, before shift by ZMID.*/ CALL PLOTZ(S*Z,3); /*Position the pen.*/ DIRECTION = 0; /*The way ahead is along the x-axis.*/ DZ = 1; /*The step before the kink.*/ IF SWAPXY THEN DIRECTION = -QUARTERTURN; /*Or maybe y.*/ IF SWAPXY THEN DZ = (0 - 1I); /*An x-y swap.*/ FRESHRANGE = TRUE; /*A sniffing.*/ FOR I = 1 TO N; /*The deviationism begins.*/ I1 = I/32768; I2 = MOD(I,32768); IF FOLD(I1,I2) THEN WAY = +1; ELSE WAY = -1; ND = DIRECTION + QUARTERTURN*WAY; IF ND >= FULLTURN THEN ND = ND - FULLTURN; IF ND < 0 THEN ND = ND + FULLTURN; LD = ND/QUARTERTURN; /*Select a leaf.*/ LD1 = MOD(ND + ABOUTTURN,FULLTURN); LD2 = LD1 + WAY*QUARTERTURN; /*No mod, see the FOR loop below.*/ FOR L = LD1 TO LD2 BY WAY; /*Round the kink.*/ LL = L; /*A copy to wrap into range.*/ IF LL < 0 THEN LL = LL + FULLTURN; IF LL >= FULLTURN THEN LL = LL - FULLTURN; ZL = Z + LEAF(LD,LL); /*Work along the curve.*/ CALL PLOTZ(S*ZL,2); /*Move a bit.*/ END; /*On to the next step.*/ DIRECTION = ND; /*The new direction.*/ Z = Z + DZ; /*The first half of the step that has been rounded.*/ DZ = DZ*(0 + 1I)*WAY; /*A right-angle, one way or the other.*/ Z = Z + DZ; /*Avoid the roundoff of hordes of fractional moves.*/ END; /*On to the next fold.*/ CALL PLOT(0,0,998); IF TRACERANGE THEN PUT SKIP(3) FILE(DRAGON) LIST('Dragoncurve: '); IF TRACERANGE THEN PUT FILE(DRAGON) DATA(RANGE,ORDER,S,ZMID);XX:END; END DRAGONCURVE; %PAGE; %PAGE; %PAGE; RANDOM:PROCEDURE(SEED) RETURNS(REAL); DECLARE SEED INTEGER; SEED = SEED*497 + 4032; IF SEED <= 0 THEN SEED = SEED + 32767; IF SEED > 32767 THEN SEED = MOD(SEED,32767); RETURN(SEED/32767.0); END RANDOM; %PAGE; TRACE:PROCEDURE(O,R,A,N,G); DECLARE (I,N,G) INTEGER; DECLARE (O,R,A(*),X0,X1,X2) COMPLEX; X1 = O + R*A(1); X0 = X1; CALL PLOT(REAL(X1),IMAG(X1),3); FOR I = 2 TO N; X2 = O + R*A(I); CALL PLOT(REAL(X2),IMAG(X2),2); X1 = X2; END; CALL PLOT(REAL(X0),IMAG(X0),2); END TRACE; CENTREZ:PROCEDURE(A,N); DECLARE (A(*),T) COMPLEX; DECLARE (I,N) INTEGER; T = 0; FOR I = 1 TO N; T = T + A(I); END; T = T/N; FOR I = 1 TO N; A(I) = A(I) - T; END; END CENTREZ; %PAGE; %PAGE; DECLARE (BELCH,ORDER,CHASE,TWIRL) INTEGER; DECLARE HOP BOOLEAN; TWOPI = 8*ATAN(1); TORAD = TWOPI/360; BELCH = REPLYN('How many dragoncurves (max 20)'); IF BELCH < 12 THEN HOP = FALSE; ELSE HOP = YEA('Go directly to order ' || IFMT(BELCH));/*ORDER = REPLYN('The depth of recursion (eg 4)'); CHASE = REPLYN('How many pursuits'); TWIRL = REPLYN('How many twirls'); TRACERANGE = YEA('Trace the ranges');*/ CALL DRAGONCURVE(BELCH,HOP);/*CALL TRIANGLEPLEX(ORDER); CALL SQUAREBASH(ORDER,+1); CALL SQUAREBASH(ORDER,-1); CALL SNOWFLAKE(ORDER); CALL SNOWFLAKE3(ORDER); CALL PURSUE(CHASE); CALL LISSAJOU(TWIRL); CALL CARDIOD; CALL HEART;*/ CALL PLOT(0,0,-3); CALL PLOT(0,0,999);END TEST;  ## PostScript %!PS%%BoundingBox: 0 0 550 400/ifpendown false def/rotation 0 def/srootii 2 sqrt def/turn { rotation add /rotation exch def } def/forward { dup rotation cos mul exch rotation sin mul ifpendown { rlineto } { rmoveto } ifelse } def/penup { /ifpendown false def } def/pendown { /ifpendown true def } def /dragon { % [ length, split, d ] dup dup 1 get 0 eq { 0 get forward } { dup 2 get 45 mul turn dup aload pop pop 1 sub exch srootii div exch 1 3 array astore dragon pop dup 2 get 90 mul neg turn dup aload pop pop 1 sub exch srootii div exch -1 3 array astore dragon dup 2 get 45 mul turn } ifelse pop } def150 150 moveto pendown [ 300 12 1 ] dragon stroke% 0 0 moveto 550 0 rlineto 0 400 rlineto -550 0 rlineto closepath stroke showpage%%END Or (almost) verbatim string rewrite: (this is a 20 page document, and don't try to print it, or you might have a very angry printer). %!PS-Adobe-3.0%%BoundingBox 0 0 300 300 /+ { 90 rotate } def/- {-90 rotate } def/!1 { dup 1 sub dup 0 eq not } def /F { 180 0 rlineto } def/X { !1 { X + Y F + } if pop } def/Y { !1 { - F X - Y } if pop } def /dragon { gsave 70 180 moveto dup 1 sub { 1 2 div sqrt dup scale -45 rotate } repeat F X stroke grestore} def 1 1 20 { dragon showpage } for %%EOF See also ## POV-Ray Example code recursive and iterative can be found at Courbe du Dragon. ## Prolog Works with SWI-Prolog which has a Graphic interface XPCE. DCG are used to compute the list of "turns" of the Dragon Curve and the list of points. dragonCurve(N) :- dcg_dg(N, [left], DCL, []), Side = 4, Angle is -N * (pi/4), dcg_computePath(Side, Angle, DCL, point(180,400), P, []), new(D, window('Dragon Curve')), send(D, size, size(800,600)), new(Path, path(poly)), send_list(Path, append, P), send(D, display, Path), send(D, open). % compute the list of points of the Dragon Curvedcg_computePath(Side, Angle, [left | DCT], point(X1, Y1)) --> [point(X1, Y1)], { X2 is X1 + Side * cos(Angle), Y2 is Y1 + Side * sin(Angle), Angle1 is Angle + pi / 2 }, dcg_computePath(Side, Angle1, DCT, point(X2, Y2)). dcg_computePath(Side, Angle, [right | DCT], point(X1, Y1)) --> [point(X1, Y1)], { X2 is X1 + Side * cos(Angle), Y2 is Y1 + Side * sin(Angle), Angle1 is Angle - pi / 2 }, dcg_computePath(Side, Angle1, DCT, point(X2, Y2)). dcg_computePath(_Side, _Angle, [], point(X1, Y1)) --> [ point(X1, Y1)]. % compute the list of the "turns" of the Dragon Curvedcg_dg(1, L) --> L. dcg_dg(N, L) --> {dcg_dg(L, L1, []), N1 is N - 1}, dcg_dg(N1, L1). % one interation of the processdcg_dg(L) --> L, [left], inverse(L). inverse([H | T]) --> inverse(T), inverse(H). inverse([]) --> []. inverse(left) --> [right]. inverse(right) --> [left]. Output : 1 ?- dragonCurve(13). true  ## PureBasic #SqRt2 = 1.4142136#SizeH = 800: #SizeV = 550Global angle.d, px, py, imageNum Procedure turn(degrees.d) angle + degrees * #PI / 180EndProcedure Procedure forward(length.d) Protected w = Cos(angle) * length Protected h = Sin(angle) * length LineXY(px, py, px + w, py + h, RGB(255,255,255)) px + w: py + hEndProcedure Procedure dragon(length.d, split, d.d) If split = 0 forward(length) Else turn(d * 45) dragon(length / #SqRt2, split - 1, 1) turn(-d * 90) dragon(length / #SqRt2, split - 1, -1) turn(d * 45) EndIfEndProcedure OpenWindow(0, 0, 0, #SizeH, #SizeV, "DragonCurve", #PB_Window_SystemMenu)imageNum = CreateImage(#PB_Any, #SizeH, #SizeV, 32)ImageGadget(0, 0, 0, 0, 0, ImageID(imageNum)) angle = 0: px = 185: py = 190If StartDrawing(ImageOutput(imageNum)) dragon(400, 15, 1) StopDrawing() SetGadgetState(0, ImageID(imageNum))EndIf Repeat: Until WaitWindowEvent(10) = #PB_Event_CloseWindow ## Python Translation of: Logo Library: turtle from turtle import * def dragon(step, length): dcr(step, length) def dcr(step, length): step -= 1 length /= 1.41421 if step > 0: right(45) dcr(step, length) left(90) dcl(step, length) right(45) else: right(45) forward(length) left(90) forward(length) right(45) def dcl(step, length): step -= 1 length /= 1.41421 if step > 0: left(45) dcr(step, length) right(90) dcl(step, length) left(45) else: left(45) forward(length) right(90) forward(length) left(45) A more pythonic version: from turtle import right, left, forward, speed, exitonclick, hideturtle def dragon(level=4, size=200, zig=right, zag=left): if level <= 0: forward(size) return size /= 1.41421 zig(45) dragon(level-1, size, right, left) zag(90) dragon(level-1, size, left, right) zig(45) speed(0)hideturtle()dragon(6)exitonclick() # click to exit Other version: from turtle import right, left, forward, speed, exitonclick, hideturtle def dragon(level=4, size=200, direction=45): if level: right(direction) dragon(level-1, size/1.41421356237, 45) left(direction * 2) dragon(level-1, size/1.41421356237, -45) right(direction) else: forward(size) speed(0)hideturtle()dragon(6)exitonclick() # click to exit ## R ### Version #1.  Dragon<-function(Iters){ Rotation<-matrix(c(0,-1,1,0),ncol=2,byrow=T) ########Rotation multiplication matrix Iteration<-list() ###################################Set up list for segment matrices for 1st Iteration[[1]] <- matrix(rep(0,16), ncol = 4) Iteration[[1]][1,]<-c(0,0,1,0) Iteration[[1]][2,]<-c(1,0,1,-1) Moveposition<-rep(0,Iters) ##########################Which point should be shifted to origin Moveposition[1]<-4 if(Iters > 1){#########################################where to move to get to origin for(l in 2:Iters){#####################################only if >1, because 1 set before for loop Moveposition[l]<-(Moveposition[l-1]*2)-2#############sets vector of all positions in matrix where last point is }} Move<-list() ########################################vector to add to all points to shift start at originfor (i in 1:Iters){half<-dim(Iteration[[i]])[1]/2half<-1:halffor(j in half){########################################Rotate all points 90 degrees clockwise Iteration[[i]][j+length(half),]<-c(Iteration[[i]][j,1:2]%*%Rotation,Iteration[[i]][j,3:4]%*%Rotation)}Move[[i]]<-matrix(rep(0,4),ncol=4)Move[[i]][1,1:2]<-Move[[i]][1,3:4]<-(Iteration[[i]][Moveposition[i],c(3,4)]*-1)Iteration[[i+1]]<-matrix(rep(0,2*dim(Iteration[[i]])[1]*4),ncol=4)##########move the dragon, set next Iteration's matrixfor(k in 1:dim(Iteration[[i]])[1]){#########################################move dragon by shifting all previous iterations point Iteration[[i+1]][k,]<-Iteration[[i]][k,]+Move[[i]]###so the start is at the origin}xlimits<-c(min(Iteration[[i]][,3])-2,max(Iteration[[i]][,3]+2))#Plotylimits<-c(min(Iteration[[i]][,4])-2,max(Iteration[[i]][,4]+2))plot(0,0,type='n',axes=FALSE,xlab="",ylab="",xlim=xlimits,ylim=ylimits)s<-dim(Iteration[[i]])[1]s<-1:ssegments(Iteration[[i]][s,1], Iteration[[i]][s,2], Iteration[[i]][s,3], Iteration[[i]][s,4], col= 'red')}}#########################################################################  ### Version #2. Note: This algorithm in R works only for orders <= 16. For bigger values it returns error in bitwAnd() [bit-wise AND]. It means: 32-bit integer is not long enough. This is true even on 64-bit computer. See samples using the same algorithm in JavaScript version #2 (order is up to 25, may be even greater). Translation of: JavaScript v.#2 Works with: R version 3.3.1 and above File:DCR7.png Output DCR7.png File:DCR13.png Output DCR13.png File:DCR16.png Output DCR16.png  # Generate and plot Dragon curve.# translation of JavaScript v.#2: http://rosettacode.org/wiki/Dragon_curve#JavaScript# 2/27/16 aev # gpDragonCurve(ord, clr, fn, d, as, xsh, ysh)# Where: ord - order (defines the number of line segments); # clr - color, fn - file name (.ext will be added), d - segment length,# as - axis scale, xsh - x-shift, ysh - y-shiftgpDragonCurve <- function(ord, clr, fn, d, as, xsh, ysh) { cat(" *** START:", date(), "order=",ord, "color=",clr, "\n"); d=10; m=640; ms=as*m; n=bitwShiftL(1, ord); c=c1=c2=c2x=c2y=i1=0; x=y=x1=y1=0; if(fn=="") {fn="DCR"} pf=paste0(fn, ord, ".png"); ttl=paste0("Dragon curve, ord=",ord); cat(" *** Plot file -", pf, "title:", ttl, "n=",n, "\n"); plot(NA, xlim=c(-ms,ms), ylim=c(-ms,ms), xlab="", ylab="", main=ttl); for (i in 0:n) { segments(x1+xsh, y1+ysh, x+xsh, y+ysh, col=clr); x1=x; y1=y; c1=bitwAnd(c, 1); c2=bitwAnd(c, 2); c2x=d; if(c2>0) {c2x=(-1)*d}; c2y=(-1)*c2x; if(c1>0) {y=y+c2y} else {x=x+c2x} i1=i+1; ii=bitwAnd(i1, -i1); c=c+i1/ii; } dev.copy(png, filename=pf, width=m, height=m); # plot to png-file dev.off(); graphics.off(); # Cleaning cat(" *** END:",date(),"\n");}## Testing samples:gpDragonCurve(7, "red", "", 20, 0.2, -30, -30)##gpDragonCurve(11, "red", "", 10, 0.6, 100, 200)gpDragonCurve(13, "navy", "", 10, 1, 300, -200)##gpDragonCurve(15, "darkgreen", "", 10, 2, -450, -500)gpDragonCurve(16, "darkgreen", "", 10, 3, -1050, -500)  Output: > gpDragonCurve(7, "red", "", 20, 0.2, -30, -30) *** START: Mon Feb 27 12:53:57 2017 order= 7 color= red *** Plot file - DCR7.png title: Dragon curve, ord=7 n= 128 *** END: Mon Feb 27 12:53:57 2017 > gpDragonCurve(13, "navy", "", 10, 1, 300, -200) *** START: Mon Feb 27 12:44:04 2017 order= 13 color= navy *** Plot file - DCR13.png title: Dragon curve, ord=13 n= 8192 *** END: Mon Feb 27 12:44:06 2017 > gpDragonCurve(16, "darkgreen", "", 10, 3, -1050, -500) *** START: Mon Feb 27 12:18:56 2017 order= 16 color= darkgreen *** Plot file - DCR16.png title: Dragon curve, ord=16 n= 65536 *** END: Mon Feb 27 12:19:03 2017  ## Racket #lang racket (require plot) (define (dragon-turn n) (if (> (bitwise-and (arithmetic-shift (bitwise-and n (- n)) 1) n) 0) 'L 'R)) (define (rotate heading dir) (cond [(eq? dir 'R) (cond [(eq? heading 'N) 'E] [(eq? heading 'E) 'S] [(eq? heading 'S) 'W] [(eq? heading 'W) 'N])] [(eq? dir 'L) (cond [(eq? heading 'N) 'W] [(eq? heading 'E) 'N] [(eq? heading 'S) 'E] [(eq? heading 'W) 'S])]))(define (step pos heading) (cond [(eq? heading 'N) (list (car pos) (add1 (cadr pos)))] [(eq? heading 'E) (list (add1 (car pos)) (cadr pos))] [(eq? heading 'S) (list (car pos) (sub1 (cadr pos)))] [(eq? heading 'W) (list (sub1 (car pos)) (cadr pos))] )) (let-values ([(dir pos trail) (for/fold ([dir 'N] [pos (list 0 0)] [trail '((0 0))]) ([n (in-range 0 50000)]) (let* ([new-dir (rotate dir (dragon-turn n))] [new-pos (step pos new-dir)]) (values new-dir new-pos (cons new-pos trail))))]) (plot-file (lines trail) "dragon.png" 'png)) ## RapidQ Translation of: BASIC This implementation displays the Dragon Curve fractal in a GUI window. DIM angle AS DoubleDIM x AS Double, y AS DoubleDECLARE SUB PaintCanvas CREATE form AS QForm Width = 800 Height = 600 CREATE canvas AS QCanvas Height = form.ClientHeight Width = form.ClientWidth OnPaint = PaintCanvas END CREATEEND CREATE SUB turn (degrees AS Double) angle = angle + degrees*3.14159265/180END SUB SUB forward (length AS Double) x2 = x + cos(angle)*length y2 = y + sin(angle)*length canvas.Line(x, y, x2, y2, &Haaffff) x = x2: y = y2END SUB SUB dragon (length AS Double, split AS Integer, d AS Double) IF split=0 THEN forward length ELSE turn d*45 dragon length/1.4142136, split-1, 1 turn -d*90 dragon length/1.4142136, split-1, -1 turn d*45 END IFEND SUB SUB PaintCanvas canvas.FillRect(0, 0, canvas.Width, canvas.Height, &H102800) x = 220: y = 220: angle = 0 dragon 384, 12, 1END SUB form.ShowModal ## REXX This REXX version uses a unique plot character to indicate which part of the dragon curve is being shown; the number of "parts" of the dragon curve can be specified (the 1st argument). The initial (facing) direction may be specified (North, East, South, or West) (the 2nd argument). A specific plot character can be specified instead for all curve parts (the 3rd argument). This, in effect, allows the dragon curve to be plotted/displayed with a different (starting) orientation. /*REXX program creates & draws an ASCII Dragon Curve (or Harter-Heighway dragon curve).*/d.=1; d.L=-d.; @.=' '; x=0; x2=x; y=0; y2=y; z=d.; @.x.y="∙"plot_pts = '123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZΘ' /*plot chars*/minX=0; maxX=0; minY=0; maxY=0 /*assign various constants & variables.*/parse arg # p c . /*#: number of iterations; P=init dir.*/if #=='' | #=="," then #=11 /*Not specified? Then use the default.*/if p=='' | p=="," then p= 'north'; upper p /* " " " " " " */if c=='' then c=plot_pts /* " " " " " " */if length(c)==2 then c=x2c(c) /*was a hexadecimal code specified? */if length(c)==3 then c=d2c(c) /* " " decimal " " */p=translate(left(p,1), 0123, 'NESW');=       /*get the orientation for dragon curve.*/     do #; $=$'R'reverse(translate($,"RL",'LR')) /*create the start of a dragon curve. */ end /*#*/ /*append char, flip, and then reverse.*/ /* [↓] create the rest of dragon curve*/ do j=1 for length($);       _=substr($,j,1) /*get next cardinal direction for curve*/ p= (p+d._)//4; if p<0 then p=p+4 /*move dragon curve in a new direction.*/ if p==0 then do; y=y+1; y2=y+1; end /*curve is going east cartologically.*/ if p==1 then do; x=x+1; x2=x+1; end /* " " south " */ if p==2 then do; y=y-1; y2=y-1; end /* " " west " */ if p==3 then do; x=x-1; x2=x-1; end /* " " north " */ if j>2**z then z=z+1 /*identify a part of curve being built.*/ !=substr(c,z,1); if !==' ' then !=right(c,1) /*choose plot point character (glyph). */ @.x.y=!; @.x2.y2=! /*draw part of the dragon curve. */ minX=min(minX,x,x2); maxX=max(maxX,x,x2); x=x2 /*define the min & max X graph limits*/ minY=min(minY,y,y2); maxY=max(maxY,y,y2); y=y2 /* " " " " " Y " " */ end /*j*/ /* [↑] process all of$  char string.*/             do r=minX  to maxX;    a=           /*nullify the line that will be drawn. */                do c=minY  to maxY; a=a || @.r.c /*create a line (row) of curve points. */                end   /*c*/                      /* [↑] append a single column of a row.*/             if a\=''  then say strip(a, "T")    /*display a line (row) of curve points.*/             end      /*r*/                      /*stick a fork in it,  we're all done. */

Choosing a   high visibility   glyph can really help make the dragon much more viewable;   the
solid fill ASCII character   (█   or   hexadecimal   db   in code page 437)   is quite good for this.

output   when using the following input:   12   south   db
(Shown at   1/6   size)

                                          ███ ███         ███ ███                                         ███ ███         ███ ███
█ █ █ █         █ █ █ █                                         █ █ █ █         █ █ █ █
█████████       █████████                                       █████████       █████████
█ █ █ █         █ █ █ █                                         █ █ █ █         █ █ █ █
███ █████ ███   ███ █████ ███                                   ███ █████ ███   ███ █████ ███
█ █ █ █         █ █ █ █                                         █ █ █ █         █ █ █ █
█████████       █████████                                       █████████       █████████
█ █ █ █         █ █ █ █                                         █ █ █ █         █ █ █ █
███ ███ ███████████ ███ █████████                               ███ ███ ███████████ ███ █████████
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █                                 █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█████████████████████████████████                               █████████████████████████████████
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █                                 █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
███ █████████████████████████████ ███                           ███ █████████████████████████████ ███
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █                                 █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█████████████████████████████████                               █████████████████████████████████
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █                                 █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█████████ ███ ███████████████████       ███ ███                 █████████ ███ ███████████████████       ███ ███
█ █ █ █         █ █ █ █ █ █ █ █         █ █ █ █                 █ █ █ █         █ █ █ █ █ █ █ █         █ █ █ █
█████████       █████████████████       █████████               █████████       █████████████████       █████████
█ █ █ █         █ █ █ █ █ █ █ █         █ █ █ █                 █ █ █ █         █ █ █ █ █ █ █ █         █ █ █ █
███ █████ ███   ███ █████████████ ███   ███ █████ ███           ███ █████ ███   ███ █████████████ ███   ███ █████ ███
█ █ █ █         █ █ █ █ █ █ █ █         █ █ █ █                 █ █ █ █         █ █ █ █ █ █ █ █         █ █ █ █
█████████       █████████████████       █████████               █████████       █████████████████       █████████
█ █ █ █         █ █ █ █ █ █ █ █         █ █ █ █                 █ █ █ █         █ █ █ █ █ █ █ █         █ █ █ █
███ ███       ███████████████████ ███ █████████                 ███ ███       ███████████████████ ███ █████████
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █                                 █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█████████████████████████████████                               █████████████████████████████████
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █                                 █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
███ █████████████████████████████ ███                           ███ █████████████████████████████ ███
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █                                 █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█████████████████████████████████                               █████████████████████████████████
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █                                 █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
███ ███         ███ ███         ███ ███ █████████████████████████████████       ███ ███         ███ ███ █████████████████████████ ███ ███
█ █ █ █         █ █ █ █         █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █         █ █ █ █         █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█████████       █████████       █████████████████████████████████████████       █████████       █████████████████████████████████
█ █ █ █         █ █ █ █         █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █         █ █ █ █         █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
███ █████ ███   ███ █████ ███   ███ █████████████████████████████████████ ███   ███ █████ ███   ███ █████████████████████████████ ███
█ █ █ █         █ █ █ █         █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █         █ █ █ █         █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█████████       █████████       █████████████████████████████████████████       █████████       █████████████████████████████████
█ █ █ █         █ █ █ █         █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █         █ █ █ █         █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
███ ███ ███████████ ███ ███████████ ███ ███████████████████████████████████████████ ███ ███████████ ███ █████████████████████████ ███ ███
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
███████████████████████████████████████████ ███████ ███████████████████████ ███████ █████████████████████████████████████████████
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █     █ █     █ █ █ █ █ █ █ █ █ █     █ █     █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
███ ███████████████████████████████████████   █████   █████████████████████   █████   ███████████████████████████████████████████ ███
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █     █ █     █ █ █ █ █ █ █ █ █ █     █ █     █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
███████████████████████████████████ ███     ███   █████████████████ ███     ███   ███████████████████████████████████████████████
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █                 █ █ █ █ █ █ █ █                 █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█████████ ███ ███████████████████████               █████████████████               █████████████████████████████████████████████       ███ ███
█ █ █ █         █ █ █ █ █ █ █ █ █ █ █                 █ █ █ █ █ █ █ █                 █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █         █ █ █ █
█████████       ███████████████████████   ███         █████ ███████████   ███         █████ █████████████████████████████████████       █████████
█ █ █ █         █ █ █ █ █ █ █ █ █ █ █     █ █         █ █     █ █ █ █     █ █         █ █     █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █         █ █ █ █
███ █████ ███   ███ ███████████████████   █████       █████   █████████   █████       █████   ███████████████████████████████████ ███   ███ █████ ███
█ █ █ █         █ █ █ █ █ █ █ █ █     █ █         █ █     █ █ █ █     █ █         █ █     █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █         █ █ █ █
█████████       █████████████████████ █████         ███   ███████████ █████         ███   ███████████████████████████████████████       █████████
█ █ █ █         █ █ █ █ █ █ █ █ █ █ █ █ █                 █ █ █ █ █ █ █ █                 █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █         █ █ █ █
███ ███       █████████████████████████████               █████████████████               ███████████████████████████████████████ ███ █████████
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █                 █ █ █ █ █ █ █ █                 █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
███████████ ███████ ███████ ███               █████ ███████ ███           ███ ███████████████████████████████████████████████████
█ █ █ █ █     █ █     █ █                     █ █     █ █                 █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
███ ███████   █████   █████                   █████   █████               ███████████████████████████████████████████████████████ ███
█ █ █     █ █     █ █                     █ █     █ █                 █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
███ ███     ███     ███                     ███     ███           ███ ███████████████████████████████████████████████████████████
█                                                                 █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
███ ███ █████                                                               █████████████████████████████████████████████████████ ███ ███
█ █ █ █ █ █ █                                                                 █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
███████████████   ███                                                         █████ █████████████████████████████████████████████
█ █ █ █ █ █ █     █ █                                                         █ █     █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
███ ███████████   █████                                                       █████   ███████████████████████████████████████████ ███
█ █ █ █ █     █ █                                                         █ █     █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█████████████ █████                                                         ███   ███████████████████████████████████████████████
█ █ █ █ █ █ █ █ █                                                                 █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
███ ███ █████████████████████                                                               █████████████████████████████████████ ███ ███
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █                                                                 █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
███████████████████████████ ███                                                           ███ █████████████ ███████ █████████████                                         ███     ███
█ █ █ █ █ █ █ █ █ █ █ █ █                                                                 █ █ █ █ █ █ █ █     █ █     █ █ █ █ █                                           █ █     █ █
███ ███████████████████████                                                               █████████████████   █████   ███████████ ███                                     █████   █████
█ █ █ █ █ █ █ █ █ █ █                                                                 █ █ █ █ █ █ █ █     █ █     █ █ █ █ █ █ █                                       █ █     █ █
███████████████████ ███                                                           ███ █████████████ ███     ███   ███████████████                                 ███ ███████ █████
█ █ █ █ █ █ █ █ █                                                                 █ █ █ █ █ █ █ █                 █ █ █ █ █ █ █                                   █ █ █ █ █ █ █ █
█████████ ███ ███████                   ███ ███                                     █████████████████               █████████████       ███ ███                     █████ ███ ███████
█ █ █ █         █ █ █                   █ █ █ █                                       █ █ █ █ █ █ █ █                 █ █ █ █ █         █ █ █ █                       █         █ █ █
█████████       ███████   ███           ███ █████                                     █████ ███████████   ███         █████ █████       █████████                     ███       ███████   ███
█ █ █ █         █ █ █     █ █           █     █                                       █ █     █ █ █ █     █ █         █ █     █         █ █ █ █                       █         █ █ █     █ █
███ █████ ███   ███ ███   █████         ∙     ███ ███                                 █████   █████████   █████       █████   ███ ███   ███ █████ ███                 ███ █     ███ ███   █████
█ █ █ █         █     █ █                 █ █ █                                   █ █     █ █ █ █     █ █         █ █     █ █ █         █ █ █ █                   █ █           █     █ █
█████████       █████ █████               ███████                                   ███   ███████████ █████         ███   ███████       █████████                   ███         █████ █████
█ █ █ █         █ █ █ █ █                 █ █ █                                           █ █ █ █ █ █ █ █                 █ █ █         █ █ █ █                                 █ █ █ █ █
███ ███       █████████████               █████                                           █████████████████               ███████ ███ █████████                               █████████████
█ █ █ █ █ █ █                 █                                               █ █ █ █ █ █ █ █                 █ █ █ █ █ █ █ █ █                                 █ █ █ █ █ █ █
███████████████   ███     ███ ███                                             █████ ███████ ███           ███ ███████████████████                               ███████████ ███
█ █ █ █ █ █ █     █ █     █ █ █                                               █ █     █ █                 █ █ █ █ █ █ █ █ █ █ █                                 █ █ █ █ █
███ ███████████   █████   ███████ ███                                         █████   █████               ███████████████████████ ███                           ███ ███████
█ █ █ █ █     █ █     █ █ █ █ █                                           █ █     █ █                 █ █ █ █ █ █ █ █ █ █ █ █ █                                 █ █ █
█████████████ ███████ ███████████                                           ███     ███           ███ ███████████████████████████                               ███ ███
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █                                                                   █ █ █ █ █ █ █ █ █ █ █ █ █ █ █                                 █
█████████ ███ ███████████ ███ ███                                                                   █████████████████████████████       ███ ███         ███ ███ █████
█ █ █ █         █ █ █ █                                                                               █ █ █ █ █ █ █ █ █ █ █ █ █         █ █ █ █         █ █ █ █ █ █ █
█████████       █████████                                                                             █████ █████████████████████       █████████       ███████████████   ███
█ █ █ █         █ █ █ █                                                                               █ █     █ █ █ █ █ █ █ █ █         █ █ █ █         █ █ █ █ █ █ █     █ █
███ █████ ███   ███ █████ ███                                                                         █████   ███████████████████ ███   ███ █████ ███   ███ ███████████   █████
█ █ █ █         █ █ █ █                                                                           █ █     █ █ █ █ █ █ █ █ █ █ █         █ █ █ █         █ █ █ █ █     █ █
█████████       █████████                                                                           ███   ███████████████████████       █████████       █████████████ █████
█ █ █ █         █ █ █ █                                                                                   █ █ █ █ █ █ █ █ █ █ █         █ █ █ █         █ █ █ █ █ █ █ █ █
███ ███         ███ ███                                                                                   ███████████████████████ ███ ███████████ ███ █████████████████████
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
███ █████████████ ███████ ███████████████████████ ███████ ███████ ███
█ █ █ █ █ █ █ █     █ █     █ █ █ █ █ █ █ █ █ █     █ █     █ █
█████████████████   █████   █████████████████████   █████   █████
█ █ █ █ █ █ █ █     █ █     █ █ █ █ █ █ █ █ █ █     █ █     █ █
███ █████████████ ███     ███   █████████████████ ███     ███     ███
█ █ █ █ █ █ █ █                 █ █ █ █ █ █ █ █
█████████████████               █████████████████
█ █ █ █ █ █ █ █                 █ █ █ █ █ █ █ █
█████ ███████████   ███         █████ ███████████   ███
█ █     █ █ █ █     █ █         █ █     █ █ █ █     █ █
█████   █████████   █████       █████   █████████   █████
█ █     █ █ █ █     █ █         █ █     █ █ █ █     █ █
███   ███████████ █████         ███   ███████████ █████
█ █ █ █ █ █ █ █                 █ █ █ █ █ █ █ █
█████████████████               █████████████████
█ █ █ █ █ █ █ █                 █ █ █ █ █ █ █ █
█████ ███████ ███               █████ ███████ ███
█ █     █ █                     █ █     █ █
█████   █████                   █████   █████
█ █     █ █                     █ █     █ █
███     ███                     ███     ███


## Ruby

Library: Shoes
Point = Struct.new(:x, :y)Line = Struct.new(:start, :stop) Shoes.app(:width => 800, :height => 600, :resizable => false) do   def split_segments(n)    dir = 1    @segments = @segments.inject([]) do |new, l|      a, b, c, d = l.start.x, l.start.y, l.stop.x, l.stop.y       mid_x = a + (c-a)/2.0 - (d-b)/2.0*dir      mid_y = b + (d-b)/2.0 + (c-a)/2.0*dir      mid_p = Point.new(mid_x, mid_y)       dir *= -1      new << Line.new(l.start, mid_p)      new << Line.new(mid_p, l.stop)    end  end   @segments = [Line.new(Point.new(200,200), Point.new(600,200))]  15.times do |n|    info "calculating frame #{n}"    split_segments(n)  end   stack do    @segments.each do |l|      line l.start.x, l.start.y, l.stop.x, l.stop.y    end  endend

## Run BASIC

graphic #g, 600,600RL$= "R"loc = 90pass = 0 [loop]#g "cls ; home ; north ; down ; fill black"for i =1 to len(RL$)  v = 255 * i /len(RL$) #g "color "; v; " 120 "; 255 -v #g "go "; loc if mid$(RL$,i,1) ="R" then #g "turn 90" else #g "turn -90"next i #g "color 255 120 0"#g "go "; locLR$ =""for i =len( RL$) to 1 step -1 if mid$( RL$, i, 1) ="R" then LR$ =LR$+"L" else LR$ =LR$+"R"next i RL$  = RL$+ "R" + LR$loc  = loc / 1.35pass = pass + 1render #ginput xxxcls if pass < 16 then goto [loop]end

import javax.swing.JFrameimport java.awt.Graphics class DragonCurve(depth: Int) extends JFrame(s"Dragon Curve (depth $depth)") { setBounds(100, 100, 800, 600); setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE); val len = 400 / Math.pow(2, depth / 2.0); val startingAngle = -depth * (Math.PI / 4); val steps = getSteps(depth).filterNot(c => c == 'X' || c == 'Y') def getSteps(depth: Int): Stream[Char] = { if (depth == 0) { "FX".toStream } else { getSteps(depth - 1).flatMap{ case 'X' => "XRYFR" case 'Y' => "LFXLY" case c => c.toString } } } override def paint(g: Graphics): Unit = { var (x, y) = (230, 350) var (dx, dy) = ((Math.cos(startingAngle) * len).toInt, (Math.sin(startingAngle) * len).toInt) for (c <- steps) c match { case 'F' => { g.drawLine(x, y, x + dx, y + dy) x = x + dx y = y + dy } case 'L' => { val temp = dx dx = dy dy = -temp } case 'R' => { val temp = dx dx = -dy dy = temp } } } } object DragonCurve extends App { new DragonCurve(14).setVisible(true);} ## Scilab It uses complex numbers and treats them as vectors to perform rotations of the edges of the curve around one of its ends. The output is a shown in a graphic window. n_folds=10 folds=[];folds=[0 1]; old_folds=[];vectors=[]; i=[]; for i=2:n_folds+1 curve_length=length(folds); vectors=folds(1:curve_length-1)-folds(curve_length); vectors=vectors.*exp(90/180*%i*%pi); new_folds=folds(curve_length)+vectors; j=curve_length; while j>1 folds=[folds new_folds(j-1)] j=j-1; end end scf(0); clf();xname("Dragon curve: "+string(n_folds)+" folds") plot2d(real(folds),imag(folds),5); set(gca(),"isoview","on");set(gca(),"axes_visible",["off","off","off"]); ## Seed7 $ include "seed7_05.s7i";  include "float.s7i";  include "math.s7i";  include "draw.s7i";  include "keybd.s7i"; var float: angle is 0.0;var integer: x is 220;var integer: y is 220; const proc: turn (in integer: degrees) is func  begin    angle +:= flt(degrees) * PI / 180.0  end func; const proc: forward (in float: length) is func  local    var integer: x2 is 0;    var integer: y2 is 0;  begin    x2 := x + trunc(cos(angle) * length);    y2 := y + trunc(sin(angle) * length);    lineTo(x, y, x2, y2, black);    x := x2;    y := y2;  end func; const proc: dragon (in float: length, in integer: split, in integer: direct) is func  begin    if split = 0 then      forward(length);    else      turn(direct * 45);      dragon(length/1.4142136, pred(split), 1);      turn(-direct * 90);      dragon(length/1.4142136, pred(split), -1);      turn(direct * 45);    end if;  end func; const proc: main is func  begin    screen(976, 654);    clear(curr_win, white);    KEYBOARD := GRAPH_KEYBOARD;    dragon(768.0, 14, 1);    ignore(getc(KEYBOARD));  end func;

Original source: [3]

## SequenceL

Tail-Recursive SequenceL Code:

import <Utilities/Math.sl>;import <Utilities/Conversion.sl>; initPoints := [[0,0],[1,0]]; f1(point(1)) :=	let		matrix := [[cos(45 * (pi/180)), -sin(45 * (pi/180))],				   [sin(45 * (pi/180)), cos(45 * (pi/180))]];	in		head(transpose((1/sqrt(2)) * matmul(matrix, transpose([point])))); f2(point(1)) :=	let		matrix := [[cos(135 * (pi/180)), -sin(135 * (pi/180))],				   [sin(135 * (pi/180)), cos(135 * (pi/180))]];	in		head(transpose((1/sqrt(2)) * matmul(matrix, transpose([point])))) + initPoints[2]; matmul(X(2),Y(2))[i,j] := sum(X[i,all]*Y[all,j]); entry(steps(0), maxX(0), maxY(0)) :=	let		scaleX := maxX / 1.5;		scaleY := maxY; 		shiftX := maxX / 3.0 / 1.5;		shiftY := maxY / 3.0;	in		round(run(steps, initPoints) * [scaleX, scaleY] + [shiftX, shiftY]); run(steps(0), result(2)) := 	let		next := f1(result) ++ f2(result);	in		result when steps <= 0	else		run(steps - 1, next);

C++ Driver Code:

Library: CImg
#include <iostream>#include <vector>#include "SL_Generated.h" #include "Cimg.h" using namespace cimg_library;using namespace std; int main(int argc, char** argv){	int threads = 0;	if(argc > 1) threads = atoi(argv[1]);	Sequence< Sequence<int> > result; 	sl_init(threads); 	int width = 500;	if(argc > 2) width = atoi(argv[2]);	int height = width;	if(argc > 3) height = atoi(argv[3]); 	CImg<unsigned char> visu(width, height, 1, 3, 0);	CImgDisplay draw_disp(visu); 	SLTimer compTimer;	SLTimer drawTimer; 	int steps = 0;	int maxSteps = 18;	if(argc > 4) maxSteps = atoi(argv[4]);	int waitTime = 200;	if(argc > 5) waitTime = atoi(argv[5]);	bool adding = true;	while(!draw_disp.is_closed())	{		compTimer.start();		sl_entry(steps, width, height, threads, result);		compTimer.stop(); 		drawTimer.start();		visu.fill(0); 		double thirdSize = ((result.size() / 2.0) / 3.0);		thirdSize = (int)thirdSize == 0 ? 1 : thirdSize; 		for(int i = 1; i <= result.size(); i+=2)		{			unsigned char shade = (unsigned char)(255 * ((((i / 2) % (int)thirdSize) / thirdSize)) + 0.5); 			unsigned char r = i / 2 <= thirdSize ? shade : 255/2;			unsigned char g = thirdSize < i / 2 && i / 2 <= thirdSize * 2 ? shade : 255/2;			unsigned char b = thirdSize * 2 < i / 2 && i / 2 <= thirdSize * 3 ? shade : 255/2;			const unsigned char color[] = {r,g,b}; 			visu.draw_line(result[i][1], result[i][2], 0, result[i + 1][1], result[i + 1][2], 0, color);		}		visu.display(draw_disp);		drawTimer.stop(); 		draw_disp.set_title("Dragon Curve in SequenceL: %d Threads | Steps: %d | CompTime: %f Seconds | Draw Time: %f Seconds", threads, steps, drawTimer.getTime(), compTimer.getTime()); 		if(adding) steps++;		else steps--; 		if(steps <= 0) adding = true;		else if(steps >= maxSteps) adding = false; 		draw_disp.wait(waitTime);	} 	sl_done();	return 0;}
Output:

## Sidef

Translation of: Perl
define halfpi = Num.pi/2 # Computing the dragon with a L-Systemvar dragon = 'FX'{    dragon.gsub!('X', 'x+yF+')    dragon.gsub!('Y', '-Fx-y')    dragon.tr!('xy', 'XY')} * 10 # Drawing the dragon in SVGvar (x, y) = (100, 100)var theta = 0var r = 2 print <<'EOT'<?xml version='1.0' encoding='utf-8' standalone='no'?><!DOCTYPE svg PUBLIC '-//W3C//DTD SVG 1.1//EN''http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd'><svg width='100%' height='100%' version='1.1'xmlns='http://www.w3.org/2000/svg'>EOT dragon.each { |c|    given(c) {        when ('F') {            printf("<line x1='%.0f' y1='%.0f' ", x, y)            printf("x2='%.0f' ", x += r*cos(theta))            printf("y2='%.0f' ", y += r*sin(theta))            printf("style='stroke:rgb(0,0,0);stroke-width:1'/>\n")        }        when ('+') { theta += halfpi }        when ('-') { theta -= halfpi }    }} print '</svg>'

Generates a SVG image to the standard output.

## Smalltalk

The classic book "Smalltalk-80 The Language and its Implementation" chapter 19 pages 372-3 includes a few lines for drawing the dragon curve (and the Hilbert curve too).

## SPL

Animation of dragon curve.

levels = 16level = 0step = 1>  draw(level)  level += step  ? level>levels    step = -1    level += step*2  .  ? level=0, step = 1  #.delay(1)< draw(level)=  mx,my = #.scrsize()  fs = #.min(mx,my)/2  r = fs/2^((level-1)/2)  x = mx/2+fs*#.sqrt(2)/2  y = my/2+fs/4  a = #.pi/4*(level-2)  #.scroff()  #.scrclear()  #.drawline(x,y,x,y)  ss = 2^level-1  > i, 0..ss    ? #.and(#.and(i,-i)*2,i)      a += #.pi/2    !      a -= #.pi/2    .    x += r*#.cos(a)    y += r*#.sin(a)    #.drawcolor(#.hsv2rgb(i/(ss+1)*360,1,1):3)    #.drawline(x,y)  <  #.scr().

## SVG

 This example is in need of improvement: Use the method described in #TI-89 BASIC to fit the curve neatly in the boundaries of the image.
Example rendering.

SVG does not support recursion, but it does support transformations and multiple uses of the same graphic, so the fractal can be expressed linearly in the iteration count of the fractal.

This version also places circles at the endpoints of each subdivision, size varying with the scale of the fractal, so you can see the shape of each step somewhat.

Note: Some SVG implementations, particularly rsvg (as of v2.26.0), do not correctly interpret XML namespaces; in this case, replace the “l” namespace prefix with “xlink”.

<?xml version="1.0" standalone="yes"?><!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 20010904//EN" "http://www.w3.org/TR/2001/REC-SVG-20010904/DTD/svg10.dtd"><svg xmlns="http://www.w3.org/2000/svg"      xmlns:l="http://www.w3.org/1999/xlink"     width="400" height="400">  <style type="text/css"><![CDATA[    line { stroke: black; stroke-width: .05; }    circle { fill: black; }  ]]></style> <defs>   <g id="marks">    <circle cx="0" cy="0" r=".03"/>    <circle cx="1" cy="0" r=".03"/>  </g>   <g id="l0">    <line x1="0" y1="0" x2="1" y2="0"/>    <!-- useful for studying the transformation stages:         <line x1="0.1" y1="0" x2="0.9" y2="0.1"/> -->  </g>   <!-- These are identical except for the id and href. -->  <g id="l1"> <use l:href="#l0" transform="matrix( .5 .5  -.5  .5  0 0)"/>              <use l:href="#l0" transform="matrix(-.5 .5  -.5 -.5  1 0)"/>              <use l:href="#marks"/></g>  <g id="l2"> <use l:href="#l1" transform="matrix( .5 .5  -.5  .5  0 0)"/>              <use l:href="#l1" transform="matrix(-.5 .5  -.5 -.5  1 0)"/>              <use l:href="#marks"/></g>  <g id="l3"> <use l:href="#l2" transform="matrix( .5 .5  -.5  .5  0 0)"/>              <use l:href="#l2" transform="matrix(-.5 .5  -.5 -.5  1 0)"/>              <use l:href="#marks"/></g>  <g id="l4"> <use l:href="#l3" transform="matrix( .5 .5  -.5  .5  0 0)"/>              <use l:href="#l3" transform="matrix(-.5 .5  -.5 -.5  1 0)"/>              <use l:href="#marks"/></g>  <g id="l5"> <use l:href="#l4" transform="matrix( .5 .5  -.5  .5  0 0)"/>              <use l:href="#l4" transform="matrix(-.5 .5  -.5 -.5  1 0)"/>              <use l:href="#marks"/></g>  <g id="l6"> <use l:href="#l5" transform="matrix( .5 .5  -.5  .5  0 0)"/>              <use l:href="#l5" transform="matrix(-.5 .5  -.5 -.5  1 0)"/>              <use l:href="#marks"/></g>  <g id="l7"> <use l:href="#l6" transform="matrix( .5 .5  -.5  .5  0 0)"/>              <use l:href="#l6" transform="matrix(-.5 .5  -.5 -.5  1 0)"/>              <use l:href="#marks"/></g>  <g id="l8"> <use l:href="#l7" transform="matrix( .5 .5  -.5  .5  0 0)"/>              <use l:href="#l7" transform="matrix(-.5 .5  -.5 -.5  1 0)"/>              <use l:href="#marks"/></g>  <g id="l9"> <use l:href="#l8" transform="matrix( .5 .5  -.5  .5  0 0)"/>              <use l:href="#l8" transform="matrix(-.5 .5  -.5 -.5  1 0)"/>              <use l:href="#marks"/></g></defs> <g transform="translate(100, 200) scale(200)">  <use l:href="#marks"/>  <use l:href="#l9"/></g> </svg>

## Tcl

Works with: Tcl version 8.5
Library: Tk

## zkl

Draw the curve in SVG to stdout.

Translation of: Perl 6
println(0'|<?xml version='1.0' encoding='utf-8' standalone='no'?>|"\n"   0'|<!DOCTYPE svg PUBLIC '-//W3C//DTD SVG 1.1//EN'|"\n"   0'|'http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd'>|"\n"   0'|<svg width='100%' height='100%' version='1.1'|"\n"   0'|xmlns='http://www.w3.org/2000/svg'>|); order:=13.0; # akin to number of recursion stepsd_size:=1000.0; # size in pixelspi:=(1.0).pi;turn_angle:=pi/2; # turn angle of each segment, 90 degrees for the canonical dragon angle:=pi - (order * (pi/4)); # starting anglelen:=(d_size/1.5) / (2.0).sqrt().pow(order); # size of each segmentx:=d_size*5/6; y:=d_size*1/3; # starting point foreach i in ([0 .. (2.0).pow(order-1)]){   # find which side to turn based on the iteration   angle += i.bitAnd(-i).shiftLeft(1).bitAnd(i) and -turn_angle or turn_angle;    dx:=x + len * angle.sin(); dy:=y - len * angle.cos();   println("<line x1='",x,"' y1='",y,"' x2='",dx,"' y2='",dy,           "' style='stroke:rgb(0,0,0);stroke-width:1'/>");   x=dx; y=dy;}println("</svg>");
Output:
$zkl bbb > dragon.svg$ls -l dragon.svg
... 408780 May 18 00:29 dragon.svg
\$less dragon.svg
<?xml version='1.0' encoding='utf-8' standalone='no'?>
<!DOCTYPE svg PUBLIC '-//W3C//DTD SVG 1.1//EN'
'http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd'>
<svg width='100%' height='100%' version='1.1'
xmlns='http://www.w3.org/2000/svg'>
<line x1='833.333' y1='333.333' x2='838.542' y2='328.125' style='stroke:rgb(0,0,0);stroke-width:1'/>
....
Visiting file:///home/craigd/Projects/ZKL/Tmp/dragon.svg shows a nice dragon curve


## ZX Spectrum Basic

Translation of: BASIC256
10 LET level=15: LET insize=12020 LET x=80: LET y=7030 LET iters=2^level40 LET qiter=256/iters50 LET sq=SQR (2): LET qpi=PI/460 LET rotation=0: LET iter=0: LET rq=170 DIM r(level)75 GO SUB 80: STOP 80 REM Dragon90 IF level>1 THEN GO TO 200100 LET yn=SIN (rotation)*insize+y110 LET xn=COS (rotation)*insize+x120 PLOT x,y: DRAW xn-x,yn-y130 LET iter=iter+1140 LET x=xn: LET y=yn150 RETURN 200 LET insize=insize/sq210 LET rotation=rotation+rq*qpi220 LET level=level-1230 LET r(level)=rq: LET rq=1240 GO SUB 80250 LET rotation=rotation-r(level)*qpi*2260 LET rq=-1270 GO SUB 80280 LET rq=r(level)290 LET rotation=rotation+rq*qpi300 LET level=level+1310 LET insize=insize*sq320 RETURN