Sierpinski square curve: Difference between revisions

Content added Content deleted
(→‎{{header|Julia}}: mark as incorrect, since it does not generate the Sierpinski square curve)
(Go/Julia moved, Phix replaced, see talk page)
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Produce a graphical or ASCII-art representation of a [[wp:Sierpiński_curve|Sierpinski square curve]] of at least order 3.
Produce a graphical or ASCII-art representation of a [[wp:Sierpiński_curve|Sierpinski square curve]] of at least order 3.


=={{header|Go}}==
{{libheader|Go Graphics}}
{{trans|Phix}}
A partial translation anyway which produces a static image of a SSC of level 5, yellow on blue, which can be viewed with a utility such as EOG.
<lang go>package main

import (
"github.com/fogleman/gg"
"math"
)

var (
width = 770.0
height = 770.0
dc = gg.NewContext(int(width), int(height))
)

var cx, cy, h float64

func lineTo(newX, newY float64) {
dc.LineTo(newX-width/2+h, height-newY+2*h)
cx, cy = newX, newY
}

func lineN() { lineTo(cx, cy-2*h) }
func lineS() { lineTo(cx, cy+2*h) }
func lineE() { lineTo(cx+2*h, cy) }
func lineW() { lineTo(cx-2*h, cy) }

func lineNW() { lineTo(cx-h, cy-h) }
func lineNE() { lineTo(cx+h, cy-h) }
func lineSE() { lineTo(cx+h, cy+h) }
func lineSW() { lineTo(cx-h, cy+h) }

func sierN(level int) {
if level == 1 {
lineNE()
lineN()
lineNW()
} else {
sierN(level - 1)
lineNE()
sierE(level - 1)
lineN()
sierW(level - 1)
lineNW()
sierN(level - 1)
}
}

func sierE(level int) {
if level == 1 {
lineSE()
lineE()
lineNE()
} else {
sierE(level - 1)
lineSE()
sierS(level - 1)
lineE()
sierN(level - 1)
lineNE()
sierE(level - 1)
}
}

func sierS(level int) {
if level == 1 {
lineSW()
lineS()
lineSE()
} else {
sierS(level - 1)
lineSW()
sierW(level - 1)
lineS()
sierE(level - 1)
lineSE()
sierS(level - 1)
}
}

func sierW(level int) {
if level == 1 {
lineNW()
lineW()
lineSW()
} else {
sierW(level - 1)
lineNW()
sierN(level - 1)
lineW()
sierS(level - 1)
lineSW()
sierW(level - 1)
}
}

func squareCurve(level int) {
sierN(level)
lineNE()
sierE(level)
lineSE()
sierS(level)
lineSW()
sierW(level)
lineNW()
lineNE() // needed to close the square in the top left hand corner
}

func main() {
dc.SetRGB(0, 0, 1) // blue background
dc.Clear()
level := 5
cx, cy = width/2, height
h = cx / math.Pow(2, float64(level+1))
squareCurve(level)
dc.SetRGB255(255, 255, 0) // yellow curve
dc.SetLineWidth(2)
dc.Stroke()
dc.SavePNG("sierpinski_square_curve.png")
}</lang>

=={{header|Julia}}==
{{incorrect||Does not generate the Sierpinski '''square''' curve}}
Modified from [https://craftofcoding.wordpress.com/2018/05/08/recursive-patterns-the-sierpinski-curve/ Craft of Coding blog, Processing version]
<lang Julia>using Luxor

function sierpinski_curve(x0, y0, h, level)
x1, y1 = x0, y0
lineto(x, y) = begin line(Point(x1, y1), Point(x, y), :stroke); x1, y1 = x, y end
lineN() = lineto(x1,y1-2*h)
lineS() = lineto(x1,y1+2*h)
lineE() = lineto(x1+2*h,y1)
lineW() = lineto(x1-2*h,y1)
lineNW() = lineto(x1-h,y1-h)
lineNE() = lineto(x1+h,y1-h)
lineSE() = lineto(x1+h,y1+h)
lineSW() = lineto(x1-h,y1+h)
function drawN(i)
if i == 1
lineNE(); lineN(); lineNW()
else
drawN(i-1); lineNE(); drawE(i-1); lineN(); drawW(i-1); lineNW(); drawN(i-1)
end
end
function drawE(i)
if i == 1
lineSE(); lineE(); lineNE()
else
drawE(i-1); lineSE(); drawS(i-1); lineE(); drawN(i-1); lineNE(); drawE(i-1)
end
end
function drawS(i)
if i == 1
lineSW(); lineS(); lineSE()
else
drawS(i-1); lineSW(); drawW(i-1); lineS(); drawE(i-1); lineSE(); drawS(i-1)
end
end
function drawW(i)
if i == 1
lineNW(); lineW(); lineSW()
else
drawW(i-1); lineNW(); drawN(i-1); lineW(); drawS(i-1); lineSW(); drawW(i-1)
end
end
function draw_curve(levl)
drawN(levl); lineNE(); drawE(levl); lineSE()
drawS(levl); lineSW(); drawW(levl); lineNW()
end
draw_curve(level)
end

Drawing(800, 800)
sierpinski_curve(10, 790, 3, 6)
finish()
preview()
</lang>


=={{header|Perl}}==
=={{header|Perl}}==
Line 276: Line 95:


=={{header|Phix}}==
=={{header|Phix}}==
<lang Phix>constant rule = "XF-F+F-XF+F+XF-F+F-X"
{{libheader|pGUI}}
string s = "F+F+XF+F+XF"
<lang Phix>-- demo\rosetta\Sierpinski_square_curve.exw
for n=1 to 4 do
--
string next = ""
-- Draws curves lo to hi (simultaneously), initially {1,1}, max {8,8}
for i=1 to length(s) do
-- Press +/- to change hi, shift +/- to change lo.
integer ch = s[i]
-- ("=_" are also mapped to "+-", for the non-numpad +/-)
next &= iff(ch='X'?rule:ch)
--
include pGUI.e

Ihandle dlg, canvas
cdCanvas cddbuffer, cdcanvas

integer width, height,
lo = 1, hi = 1
atom cx, cy, h

procedure lineTo(atom newX, newY)
cdCanvasVertex(cddbuffer, newX-width/2+h, height-newY+2*h)
cx = newX
cy = newY
end procedure

procedure lineN() lineTo(cx,cy-2*h) end procedure
procedure lineS() lineTo(cx,cy+2*h) end procedure
procedure lineE() lineTo(cx+2*h,cy) end procedure
procedure lineW() lineTo(cx-2*h,cy) end procedure
procedure lineNW() lineTo(cx-h,cy-h) end procedure
procedure lineNE() lineTo(cx+h,cy-h) end procedure
procedure lineSE() lineTo(cx+h,cy+h) end procedure
procedure lineSW() lineTo(cx-h,cy+h) end procedure

procedure sierN(integer level)
if level=1 then
lineNE() lineN()
lineNW()
else
sierN(level-1) lineNE()
sierE(level-1) lineN()
sierW(level-1) lineNW()
sierN(level-1)
end if
end procedure
procedure sierE(integer level)
if level=1 then
lineSE() lineE()
lineNE()
else
sierE(level-1) lineSE()
sierS(level-1) lineE()
sierN(level-1) lineNE()
sierE(level-1)
end if
end procedure
procedure sierS(integer level)
if level=1 then
lineSW() lineS()
lineSE()
else
sierS(level-1) lineSW()
sierW(level-1) lineS()
sierE(level-1) lineSE()
sierS(level-1)
end if
end procedure
procedure sierW(integer level)
if level=1 then
lineNW() lineW()
lineSW()
else
sierW(level-1) lineNW()
sierN(level-1) lineW()
sierS(level-1) lineSW()
sierW(level-1)
end if
end procedure

procedure sierpinskiCurve(integer level)
sierN(level) lineNE()
sierE(level) lineSE()
sierS(level) lineSW()
sierW(level) lineNW()
end procedure

function redraw_cb(Ihandle /*ih*/, integer /*posx*/, integer /*posy*/)
{width, height} = IupGetIntInt(canvas, "DRAWSIZE")
cdCanvasActivate(cddbuffer)
for level=lo to hi do
cx = width/2
cy = height
h = cx/power(2,level+1)
cdCanvasBegin(cddbuffer, CD_CLOSED_LINES)
sierpinskiCurve(level)
cdCanvasEnd(cddbuffer)
end for
end for
s = next
cdCanvasFlush(cddbuffer)
end for
return IUP_DEFAULT
end function

function map_cb(Ihandle ih)
cdcanvas = cdCreateCanvas(CD_IUP, ih)
cddbuffer = cdCreateCanvas(CD_DBUFFER, cdcanvas)
cdCanvasSetBackground(cddbuffer, CD_WHITE)
cdCanvasSetForeground(cddbuffer, CD_BLUE)
return IUP_DEFAULT
end function

function key_cb(Ihandle /*ih*/, atom c)
if c=K_ESC then return IUP_CLOSE end if
if find(c,"+=-_") then
bool bShift = IupGetInt(NULL,"SHIFTKEY")
if c='+' or c='=' then
if bShift then
lo = min(lo+1,hi)
else
hi = min(8,hi+1)
end if
elsif c='-' or c='_' then
if bShift then
lo = max(1,lo-1)
else
hi = max(lo,hi-1)
end if
end if
IupSetStrAttribute(dlg, "TITLE", "Sierpinski square curve (%d..%d)",{lo,hi})
cdCanvasClear(cddbuffer)
IupUpdate(canvas)
end if
return IUP_CONTINUE
end function

procedure main()
IupOpen()
canvas = IupCanvas(NULL)
IupSetAttribute(canvas, "RASTERSIZE", "770x770")
IupSetCallback(canvas, "MAP_CB", Icallback("map_cb"))
IupSetCallback(canvas, "ACTION", Icallback("redraw_cb"))

dlg = IupDialog(canvas)
IupSetAttribute(dlg, "TITLE", "Sierpinski square curve (1..1)")
IupSetCallback(dlg, "K_ANY", Icallback("key_cb"))

IupMap(dlg)
IupShowXY(dlg,IUP_CENTER,IUP_CENTER)
IupMainLoop()
IupClose()
end procedure


sequence X = {}, Y= {}
main()</lang>
atom x=0, y=0, theta=PI/4, r = 6
string svg = ""
for i=1 to length(s) do
integer ch = s[i]
switch ch do
case 'F': X &= x; x += r*cos(theta)
Y &= y; y += r*sin(theta)
case '+': theta += PI/2
case '-': theta -= PI/2
end switch
end for
constant svgfmt = """
<svg xmlns="http://www.w3.org/2000/svg" height="%d" width="%d">
<rect height="100%%" width="100%%" style="fill:black" />
<polyline points="%s" style="stroke: orange; stroke-width: 1" transform="translate(%d,%d)" />
</svg>"""
string points = ""
for i=1 to length(X) do
points &= sprintf("%.2f,%.2f ",{X[i],Y[i]})
end for
integer fn = open("sierpinski_square_curve.svg","w")
atom xt = -min(X)+10,
yt = -min(Y)+10
printf(fn,svgfmt,{max(X)+xt+10,max(Y)+yt+10,points,xt,yt})
close(fn)</lang>


=={{header|Sidef}}==
=={{header|Sidef}}==
Retrieved from "https://rosettacode.org/wiki/Sierpinski_square_curve"