Feigenbaum constant calculation: Difference between revisions

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{{draft task}}
 
 
;Task:
Line 13 ⟶ 12:
{{trans|Python}}
 
<langsyntaxhighlight lang="11l">V max_it = 13
V max_it_j = 10
V a1 = 1.0
Line 34 ⟶ 33:
d1 = d
a2 = a1
a1 = a</langsyntaxhighlight>
 
{{out}}
<pre>
i d
2 3.21851142
3 4.38567760
4 4.60094928
5 4.65513050
6 4.66611195
7 4.66854858
8 4.66906066
9 4.66917155
10 4.66919515
11 4.66920026
12 4.66920098
13 4.66920537
</pre>
 
=={{header|Ada}}==
{{Trans|Ring}}
<syntaxhighlight lang="ada">
with Ada.Text_IO; use Ada.Text_IO;
with Ada.Integer_Text_IO; use Ada.Integer_Text_IO;
 
procedure Main is
procedure feigenbaum is
subtype i_range is Integer range 2 .. 13;
subtype j_range is Integer range 1 .. 10;
 
-- the number of digits in type Real is reduced to 15 to produce the
-- results reported by C, C++, C# and Ring. Increasing the number of
-- digits in type Real produces the results reported by D.
 
type Real is digits 15;
package Real_Io is new Float_IO (Real);
use Real_Io;
 
a, x, y, d : Real;
a1 : Real := 1.0;
a2 : Real := 0.0;
d1 : Real := 3.2;
begin
Put_Line (" i d");
for i in i_range loop
a := a1 + (a1 - a2) / d1;
for j in j_range loop
x := 0.0;
y := 0.0;
for k in 1 .. 2**i loop
y := 1.0 - 2.0 * x * y;
x := a - x * x;
end loop;
a := a - x / y;
end loop;
d := (a1 - a2) / (a - a1);
Put (Item => i, Width => 2);
Put (Item => d, Fore => 5, Aft => 8, Exp => 0);
New_Line;
d1 := d;
a2 := a1;
a1 := a;
end loop;
end feigenbaum;
 
begin
feigenbaum;
end Main;
</syntaxhighlight>
{{out}}
<pre>
Line 56 ⟶ 122:
{{works with|ALGOL 68G|Any - tested with release 2.8.3.win32}}
{{Trans|Ring}}
<langsyntaxhighlight lang="algol68"># Calculate the Feigenbaum constant #
print( ( "Feigenbaum constant calculation:", newline ) );
Line 85 ⟶ 151:
a2 := a1;
a1 := a
OD</langsyntaxhighlight>
{{out}}
<pre>
Line 105 ⟶ 171:
 
=={{header|AWK}}==
<syntaxhighlight lang="awk">
<lang AWK>
# syntax: GAWK -f FEIGENBAUM_CONSTANT_CALCULATION.AWK
BEGIN {
Line 132 ⟶ 198:
exit(0)
}
</syntaxhighlight>
</lang>
{{out}}
<pre>
Line 149 ⟶ 215:
13 4.66920537
</pre>
 
=={{header|BASIC}}==
==={{header|BASIC256}}===
<syntaxhighlight lang="freebasic">maxIt = 13 : maxItj = 13
a1 = 1.0 : a2 = 0.0 : d = 0.0 : d1 = 3.2
 
print "Feigenbaum constant calculation:"
print
print " i d"
print "======================"
 
for i = 2 to maxIt
a = a1 + (a1 - a2) / d1
for j = 1 to maxItj
x = 0.0 : y = 0.0
for k = 1 to 2 ^ i
y = 1 - 2 * y * x
x = a - x * x
next k
a -= x / y
next j
d = (a1 - a2) / (a - a1)
print rjust(i,3); chr(9); ljust(d,13,"0")
d1 = d
a2 = a1
a1 = a
next i</syntaxhighlight>
{{out}}
<pre>Same as FreeBASIC entry.</pre>
 
==={{header|Chipmunk Basic}}===
{{works with|Chipmunk Basic|3.6.4}}
{{trans|FreeBASIC}}
<syntaxhighlight lang="qbasic">100 cls
110 mit = 13
120 mitj = 13
130 a1 = 1
140 a2 = 0
150 d = 0
160 d1 = 3.2
170 print "Feigenbaum constant calculation:"
180 print
190 print " i d"
200 print "==================="
210 for i = 2 to mit
220 a = a1+(a1-a2)/d1
230 for j = 1 to mitj
240 x = 0
250 y = 0
260 for k = 1 to 2^i
270 y = 1-2*y*x
280 x = a-x*x
290 next k
300 a = a-(x/y)
310 next j
320 d = (a1-a2)/(a-a1)
330 print using "###";i;" ";
335 print using "##.#########";d
340 d1 = d
350 a2 = a1
360 a1 = a
370 next i
380 end</syntaxhighlight>
 
==={{header|Just BASIC}}===
<syntaxhighlight lang="lb">maxit = 13 : maxitj = 13
a1 = 1.0 : a2 = 0.0 : d = 0.0 : d1 = 3.2
 
print "Feigenbaum constant calculation:"
print
print " i d"
print "==================="
 
for i = 2 to maxit
a = a1 + (a1 - a2) / d1
for j = 1 to maxitj
x = 0 : y = 0
for k = 1 to 2 ^ i
y = 1 - 2 * y * x
x = a - x * x
next k
a = a - (x / y)
next j
d = (a1 - a2) / (a - a1)
print i; tab(8); d
d1 = d
a2 = a1
a1 = a
next i</syntaxhighlight>
 
==={{header|MSX Basic}}===
{{works with|MSX BASIC|any}}
{{trans|FreeBASIC}}
<syntaxhighlight lang="qbasic">100 CLS
110 mit = 13
120 mitj = 13
130 a1 = 1
140 a2 = 0
150 d = 0
160 d1 = 3.2
170 PRINT "Feigenbaum constant calculation:"
180 PRINT
190 PRINT " i d"
200 PRINT "==================="
210 FOR i = 2 TO mit
220 a = a1 + (a1 - a2) / d1
230 FOR j = 1 TO mitj
240 x = 0
250 y = 0
260 FOR k = 1 TO 2 ^ i
270 y = 1 - 2 * y * x
280 x = a - x * x
290 NEXT k
300 a = a - (x / y)
310 NEXT j
320 d = (a1 - a2) / (a - a1)
330 PRINT USING "### ##.#########"; i; d
340 d1 = d
350 a2 = a1
360 a1 = a
370 NEXT i
380 END</syntaxhighlight>
 
==={{header|True BASIC}}===
<syntaxhighlight lang="qbasic">LET maxit = 13
LET maxitj = 13
LET a1 = 1.0
LET d1 = 3.2
 
PRINT "Feigenbaum constant calculation:"
PRINT
PRINT " i d"
PRINT "==================="
 
FOR i = 2 to maxit
LET a = a1 + (a1 - a2) / d1
FOR j = 1 to maxitj
LET x = 0
LET y = 0
FOR k = 1 to 2 ^ i
LET y = 1 - 2 * y * x
LET x = a - x * x
NEXT k
LET a = a - (x / y)
NEXT j
LET d = (a1 - a2) / (a - a1)
PRINT using "### ##.#########": i, d
LET d1 = d
LET a2 = a1
LET a1= a
NEXT i
END</syntaxhighlight>
{{out}}
<pre>Same as FreeBASIC entry.</pre>
 
==={{header|Yabasic}}===
<syntaxhighlight lang="freebasic">maxIt = 13 : maxItj = 13
a1 = 1.0 : a2 = 0.0 : d = 0.0 : d1 = 3.2
 
print "Feigenbaum constant calculation:"
print "\n i d"
print "===================="
 
for i = 2 to maxIt
a = a1 + (a1 - a2) / d1
for j = 1 to maxItj
x = 0.0 : y = 0.0
for k = 1 to 2 ^ i
y = 1 - 2 * y * x
x = a - x * x
next k
a = a - x / y
next j
d = (a1 - a2) / (a - a1)
print i using("###"), chr$(9), d
d1 = d
a2 = a1
a1 = a
next i</syntaxhighlight>
 
=={{header|C}}==
{{trans|Ring}}
<langsyntaxhighlight lang="c">#include <stdio.h>
 
void feigenbaum() {
Line 180 ⟶ 425:
feigenbaum();
return 0;
}</langsyntaxhighlight>
 
{{output}}
Line 199 ⟶ 444:
</pre>
 
=={{header|C++ sharp|C#}}==
{{trans|C}}
<lang cpp>#include <iostream>
 
int main() {
const int max_it = 13;
const int max_it_j = 10;
double a1 = 1.0, a2 = 0.0, d1 = 3.2;
 
std::cout << " i d\n";
for (int i = 2; i <= max_it; ++i) {
double a = a1 + (a1 - a2) / d1;
for (int j = 1; j <= max_it_j; ++j) {
double x = 0.0;
double y = 0.0;
for (int k = 1; k <= 1 << i; ++k) {
y = 1.0 - 2.0*y*x;
x = a - x * x;
}
a -= x / y;
}
double d = (a1 - a2) / (a - a1);
printf("%2d %.8f\n", i, d);
d1 = d;
a2 = a1;
a1 = a;
}
 
return 0;
}</lang>
{{out}}
<pre> i d
2 3.21851142
3 4.38567760
4 4.60094928
5 4.65513050
6 4.66611195
7 4.66854858
8 4.66906066
9 4.66917155
10 4.66919515
11 4.66920026
12 4.66920098
13 4.66920537</pre>
 
=={{header|C#|C sharp}}==
{{trans|Kotlin}}
<langsyntaxhighlight lang="csharp">using System;
 
namespace FeigenbaumConstant {
Line 276 ⟶ 476:
}
}
}</langsyntaxhighlight>
{{out}}
<pre> i d
2 3.21851142
3 4.38567760
4 4.60094928
5 4.65513050
6 4.66611195
7 4.66854858
8 4.66906066
9 4.66917155
10 4.66919515
11 4.66920026
12 4.66920098
13 4.66920537</pre>
 
=={{header|C++}}==
{{trans|C}}
<syntaxhighlight lang="cpp">#include <iostream>
 
int main() {
const int max_it = 13;
const int max_it_j = 10;
double a1 = 1.0, a2 = 0.0, d1 = 3.2;
 
std::cout << " i d\n";
for (int i = 2; i <= max_it; ++i) {
double a = a1 + (a1 - a2) / d1;
for (int j = 1; j <= max_it_j; ++j) {
double x = 0.0;
double y = 0.0;
for (int k = 1; k <= 1 << i; ++k) {
y = 1.0 - 2.0*y*x;
x = a - x * x;
}
a -= x / y;
}
double d = (a1 - a2) / (a - a1);
printf("%2d %.8f\n", i, d);
d1 = d;
a2 = a1;
a1 = a;
}
 
return 0;
}</syntaxhighlight>
{{out}}
<pre> i d
Line 293 ⟶ 538:
 
=={{header|D}}==
<langsyntaxhighlight lang="d">import std.stdio;
 
void main() {
Line 321 ⟶ 566:
a1 = a;
}
}</langsyntaxhighlight>
{{out}}
<pre> i d
Line 336 ⟶ 581:
12 4.66920099
13 4.66920555</pre>
 
=={{header|Delphi}}==
{{works with|Delphi|6.0}}
{{libheader|SysUtils,StdCtrls}}
Translated from Algol
<syntaxhighlight lang="Delphi">
 
 
procedure FeigenbaumConstant(Memo: TMemo);
{ Calculate the Feigenbaum constant }
const IMax = 13;
const JMax = 10;
var I,J,K: integer;
var A1,A2,D1,X,Y: double;
var A,D: double;
begin
Memo.Lines.Add('Feigenbaum constant calculation:');
{Set initial starting values for iterations}
A1:=1.0; A2:=0.0; D1:=3.2;
Memo.Lines.Add(' I A D');
for I:=2 to IMax do
begin
{Find next Bifurcation parameter, A}
A:=A1 + (A1 - A2) / D1;
for J:=1 to JMax do
begin
X:=0; Y:=0;
for K:=1 to 1 shl i do
begin
Y:=1 - 2 * y * x;
X:=A - X * X
end;
A:=A - X / Y
end;
{Use current and previous values of A}
{to calculate the Feigenbaum constant D }
D:= (A1 - A2) / (A - A1);
Memo.Lines.Add(Format('%2d %2.8f %2.8f',[I,A,D]));
D1:=D; A2:=A1; A1:=A;
end;
end;
 
</syntaxhighlight>
{{out}}
<pre>
Feigenbaum constant calculation:
I A D
2 1.31070264 3.21851142
3 1.38154748 4.38567760
4 1.39694536 4.60094928
5 1.40025308 4.65513050
6 1.40096196 4.66611195
7 1.40111380 4.66854858
8 1.40114633 4.66906066
9 1.40115329 4.66917155
10 1.40115478 4.66919515
11 1.40115510 4.66920028
12 1.40115517 4.66920099
13 1.40115519 4.66920555
</pre>
 
=={{header|EasyLang}}==
{{trans|AWK}}
<syntaxhighlight>
numfmt 6 0
a1 = 1 ; a2 = 0 ; d1 = 3.2
ipow2 = 4
for i = 2 to 13
a = a1 + (a1 - a2) / d1
for j = 1 to 10
x = 0 ; y = 0
for k = 1 to ipow2
y = 1 - 2 * y * x
x = a - x * x
.
a -= x / y
.
d = (a1 - a2) / (a - a1)
print i & " " & d
d1 = d ; a2 = a1 ; a1 = a
ipow2 *= 2
.
</syntaxhighlight>
 
=={{header|F#|F sharp}}==
{{trans|C#}}
<langsyntaxhighlight lang="fsharp">open System
 
[<EntryPoint>]
Line 363 ⟶ 691:
a2 <- a1
a1 <- a
0 // return an integer exit code</langsyntaxhighlight>
{{out}}
<pre> i d
Line 380 ⟶ 708:
 
=={{header|Factor}}==
{{trans|Perl 6Raku}}
<langsyntaxhighlight lang="factor">USING: formatting io locals math math.ranges sequences ;
 
[let
Line 405 ⟶ 733:
exp d "%2d %.8f\n" printf
] each
]</langsyntaxhighlight>
{{out}}
<pre>
Line 422 ⟶ 750:
13 4.66920537
</pre>
 
=={{header|Fōrmulæ}}==
 
In [https://wiki.formulae.org/Feigenbaum_constant_calculation this] page you can see the solution of this task.
 
Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text ([http://wiki.formulae.org/Editing_F%C5%8Drmul%C3%A6_expressions more info]). Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation &mdash;i.e. XML, JSON&mdash; they are intended for transportation effects more than visualization and edition.
 
The option to show Fōrmulæ programs and their results is showing images. Unfortunately images cannot be uploaded in Rosetta Code.
 
=={{header|Fortran}}==
<langsyntaxhighlight lang="fortran"> program feigenbaum
implicit none
 
Line 461 ⟶ 781:
print '(i4,f13.10)', i, d1
end do
end</langsyntaxhighlight>
{{out}}
<pre> i d
Line 485 ⟶ 805:
 
=={{header|FreeBASIC}}==
<langsyntaxhighlight lang="freebasic">' version 25-0-2019
' compile with: fbc -s console
 
Line 517 ⟶ 837:
Print : Print "hit any key to end program"
Sleep
End</langsyntaxhighlight>
{{out}}
<pre>Feigenbaum constant calculation:
Line 535 ⟶ 855:
12 4.669201301
13 4.669198656</pre>
 
=={{header|Fōrmulæ}}==
 
{{FormulaeEntry|page=https://formulae.org/?script=examples/Feigenbaum_constant_calculation}}
 
'''Solution'''
 
[[File:Fōrmulæ - Feigenbaum constant calculation 01.png]]
 
'''Test case'''
 
[[File:Fōrmulæ - Feigenbaum constant calculation 02.png]]
 
[[File:Fōrmulæ - Feigenbaum constant calculation 03.png]]
 
=={{header|FutureBasic}}==
{{trans|Ring and Phix}}
<syntaxhighlight lang="futurebasic">
window 1, @"Feignenbaum Constant", ( 0, 0, 200, 300 )
 
_maxIt = 13
_maxItJ = 10
 
void local fn Feignenbaum
NSUInteger i, j, k
double a1 = 1.0, a2 = 0.0, d1 = 3.2
print "Feignenbaum Constant"
print " i d"
for i = 2 to _maxIt
double a = a1 + ( a1 - a2 ) / d1
for j = 1 to _maxItJ
double x = 0, y = 0
for k = 1 to fn pow( 2, i )
y = 1 - 2 * y * x
x = a - x * x
next
a = a - x / y
next
double d = ( a1 - a2 ) / ( a - a1 )
printf @"%2d. %.8f", i, d
d1 = d
a2 = a1
a1 = a
next
end fn
 
fn Feignenbaum
 
HandleEvents
</syntaxhighlight>
 
{{out}}
<pre>
Feignenbaum Constant
i d
2 3.21851142
3 4.38567760
4 4.60094928
5 4.65513050
6 4.66611195
7 4.66854858
8 4.66906066
9 4.66917155
10 4.66919515
11 4.66920026
12 4.66920098
13 4.66920537
</pre>
 
=={{header|Go}}==
{{trans|Ring}}
<langsyntaxhighlight lang="go">package main
 
import "fmt"
Line 564 ⟶ 954:
func main() {
feigenbaum()
}</langsyntaxhighlight>
 
{{out}}
Line 582 ⟶ 972:
13 4.66920537
</pre>
 
 
=={{header|Groovy}}==
{{trans|Java}}
<syntaxhighlight lang="groovy">class Feigenbaum {
static void main(String[] args) {
int max_it = 13
int max_it_j = 10
double a1 = 1.0
double a2 = 0.0
double d1 = 3.2
double a
 
println(" i d")
for (int i = 2; i <= max_it; i++) {
a = a1 + (a1 - a2) / d1
for (int j = 0; j < max_it_j; j++) {
double x = 0.0
double y = 0.0
for (int k = 0; k < 1 << i; k++) {
y = 1.0 - 2.0 * y * x
x = a - x * x
}
a -= x / y
}
double d = (a1 - a2) / (a - a1)
printf("%2d %.8f\n", i, d)
d1 = d
a2 = a1
a1 = a
}
}
}</syntaxhighlight>
{{out}}
<pre> i d
2 3.21851142
3 4.38567760
4 4.60094928
5 4.65513050
6 4.66611195
7 4.66854858
8 4.66906066
9 4.66917155
10 4.66919515
11 4.66920026
12 4.66920098
13 4.66920537</pre>
 
=={{header|Haskell}}==
<langsyntaxhighlight lang="haskell">import Data.List (mapAccumL)
 
feigenbaumApprox :: Int -> [Double]
Line 618 ⟶ 1,055:
(show <$> feigenbaumApprox 13)
where
justifyRight n c s = drop (length s) (replicate n c ++ s)</langsyntaxhighlight>
{{Out}}
<pre> 1 3.2185114220380866
Line 633 ⟶ 1,070:
12 4.669205372040318
13 4.669207514010413</pre>
 
=={{header|J}}==
Translated from the beautiful Fōrmulæ version. Rather than a verb, the conjunction pre-assigns m and n .
<pre>
Feigenbaum =: conjunction define NB. use: n Feigenbaum m
irange=: <. + i.@:>:@:|@:- NB. inclusive range
a=. 0 1
delta=. , 3.2
for_i. 3 irange n do.
tmp=. ({: + ({:delta) *inv ({: - _2&{)) a
for. i. m do.
'b bp'=. 0
for. i. 2 ^ <: i do.
'b bp'=. (tmp - *: b) , 1 _2 p. b * bp
end.
tmp=. tmp - b % bp
end.
a=. a , tmp
delta=. delta , %/@:(-/"1) (- 2 3 ,: 1 2) { a
end.
2 14j6 14j6 ": (#\ i. # delta) ,. (}. a) ,. delta
)
 
8 Feigenbaum 13
1 1.000000 3.200000
2 1.310703 3.218511
3 1.381547 4.385678
4 1.396945 4.600949
5 1.400253 4.655130
6 1.400962 4.666112
7 1.401114 4.668549
8 1.401146 4.669061
9 1.401153 4.669172
10 1.401155 4.669195
11 1.401155 4.669200
12 1.401155 4.669201
</pre>
 
=={{header|Java}}==
{{trans|Kotlin}}
<langsyntaxhighlight lang="java">public class Feigenbaum {
public static void main(String[] args) {
int max_it = 13;
Line 664 ⟶ 1,138:
}
}
}</langsyntaxhighlight>
{{out}}
<pre> i d
Line 680 ⟶ 1,154:
13 4.66920537</pre>
 
=={{header|jq}}==
<syntaxhighlight lang="jq">def feigenbaum_delta(imax; jmax):
def lpad: tostring | (" " * (4 - length)) + .;
def pp(i;x): "\(i|lpad) \(x)";
 
"Feigenbaum's delta constant incremental calculation:",
pp("i"; "δ"),
pp(1; "3.20"),
( foreach range(2; 1+imax) as $i (
{a1: 1.0, a2: 0.0, d1: 3.2};
 
.a = .a1 + (.a1 - .a2) / .d1
| reduce range(1; 1+jmax) as $j (.;
.x = 0 | .y = 0
| reduce range(1; 1+pow(2;$i)) as $k (.;
.y = (1 - 2 * .x * .y)
| .x = .a - (.x * .x) )
| .a -= (.x / .y) )
| .d = (.a1 - .a2) / (.a - .a1)
| .d1 = .d | .a2 = .a1 | .a1 = .a;
pp($i; .d) ) ) ;
Feigenbaum_delta(13; 10)
</syntaxhighlight>
{{out}}
<syntaxhighlight lang="sh">
Feigenbaum's delta constant incremental calculation:
i δ
1 3.20
2 3.2185114220380866
3 4.3856775985683365
4 4.600949276538056
5 4.6551304953919646
6 4.666111947822846
7 4.668548581451485
8 4.66906066077106
9 4.669171554514976
10 4.669195154039278
11 4.669200256503637
12 4.669200975097843
13 4.669205372040318
</syntaxhighlight>
 
=={{header|Julia}}==
<langsyntaxhighlight lang="julia"># http://en.wikipedia.org/wiki/Feigenbaum_constant
 
function feigenbaum_delta(imax=23, jmax=20)
Line 705 ⟶ 1,221:
 
feigenbaum_delta()
</langsyntaxhighlight>{{out}}
<pre>
Feigenbaum's delta constant incremental calculation:
Line 733 ⟶ 1,249:
23 4.66920160910297781286849594159066394676896043144121209732784416240857379387701
</pre>
 
 
=={{header|Kotlin}}==
{{trans|Ring}}
<langsyntaxhighlight lang="scala">// Version 1.2.40
 
fun feigenbaum() {
Line 767 ⟶ 1,282:
fun main(args: Array<String>) {
feigenbaum()
}</langsyntaxhighlight>
 
{{output}}
Line 785 ⟶ 1,300:
13 4.66920537
</pre>
 
=={{header|Lambdatalk}}==
Following the Python code in a recursive mode.
<syntaxhighlight lang="scheme">
{feigenbaum 11} // on my computer stackoverflow for values greater than 11
-> [3.2185114220380866,4.3856775985683365,4.600949276538056,4.6551304953919646,4.666111947822846,
4.668548581451485,4.66906066077106,4.669171554514976,4.669195154039278,4.669200256503637]
 
with:
 
{def feigenbaum
{lambda {:maxi}
{f3 :maxi 10 1 0 3.2 0 {A.new} 2}}}
 
{def f3
{lambda {:maxi :maxj :a1 :a2 :d1 :a3 :s :i}
{if {< :i {+ :maxi 1}}
then {let { {:maxi :maxi} {:maxj :maxj} {:a1 :a1} {:a2 :a2}
{:a3 {f2 {+ :a1 {/ {- :a1 :a2} :d1}} :i :maxj 1} }
{:s :s} {:i :i}
} {f3 :maxi :maxj :a3 :a1 {/ {- :a1 :a2} {- :a3 :a1}} :a3
{A.addlast! {/ {- :a1 :a2} {- :a3 :a1}} :s} {+ :i 1}} }
else :s}}}
 
{def f2
{lambda {:a :i :maxj :j}
{if {< :j {+ :maxj 1}}
then {f2 {f1 :a :i 0 0 1} :i :maxj {+ :j 1}}
else :a}}}
 
{def f1
{lambda {:a :i :y :x :k}
{if {< :k {+ {pow 2 :i} 1}}
then {f1 :a :i {- 1 {* 2 :y :x}} {- :a {* :x :x}} {+ :k 1}}
else {- :a {/ :x :y}} }}}
 
</syntaxhighlight>
 
=={{header|Lua}}==
<langsyntaxhighlight lang="lua">function leftShift(n,p)
local r = n
while p>0 do
Line 821 ⟶ 1,373:
a2 = a1
a1 = a
end</langsyntaxhighlight>
{{out}}
<pre> i d
Line 836 ⟶ 1,388:
12 4.66920098
13 4.66920537</pre>
 
=={{header|M2000 Interpreter}}==
Using decimal type (26 decimal places) is better for this calculation (this has the same output as FORTRAN). Variable maxitj can be change to lower values when the i get higher value. Although we can't go lower than 2. So here we can start with 13, and lower to 2 for 16th iteration of i
 
<syntaxhighlight lang="m2000 interpreter">
module Feigenbaum_constant_calculation (maxit as integer, c as single){
locale 1033 // show dot for decimal separator symbol
single maxitj=13
integer i, j
long k
decimal a1=1, a2, d , d1=3.2, y, x, a
print "Feigenbaum constant calculation:"
print
print format$("{0:-7} {1:-12} {2}","i", "δ","max j")
for i = 2 to maxit
a=a1+(a1-a2)/d1
for j = 1 to maxitj {x=0:y=0:for k=1 to 2&^i {y=1@-2@*y*x:x=a-x*x}:a-=x/y}
d=(a1-a2)/(a-a1)
print format$("{0::-7} {1:10:-12} {2::-5}",i, d, j-1)
maxitj-=c
d1=d:a2=a1:a1= a
next
}
profiler
Feigenbaum_constant_calculation 18, .7
print timecount
</syntaxhighlight>
{{out}}
<pre>
i δ max j
2 3.2185114220 13
3 4.3856775986 12
4 4.6009492765 12
5 4.6551304954 11
6 4.6661119478 10
7 4.6685485814 10
8 4.6690606606 9
9 4.6691715554 8
10 4.6691951560 7
11 4.6692002291 7
12 4.6692013133 6
13 4.6692015458 5
14 4.6692015955 5
15 4.6692016062 4
16 4.6692016085 3
17 4.6692016090 3
18 4.6692016091 2
</pre>
 
=={{header|Mathematica}}/{{header|Wolfram Language}}==
{{trans|D}}
<syntaxhighlight lang="mathematica">maxit = 13;
maxitj = 10;
a1 = 1.0;
a2 = 0.0;
d1 = 3.2;
a = 0.0;
Table[
a = a1 + (a1 - a2)/d1;
Do[
x = 0.0;
y = 0.0;
Do[
y = 1.0 - 2.0 y x;
x = a - x x;
,
{k, 1, 2^i}
];
a = a - x/y
,
{j, maxitj}
];
d = (a1 - a2)/(a - a1);
d1 = d;
a2 = a1;
a1 = a;
{i, d}
,
{i, 2, maxit}
] // Grid</syntaxhighlight>
{{out}}
<pre>2 3.21851
3 4.38568
4 4.60095
5 4.65513
6 4.66611
7 4.66855
8 4.66906
9 4.66917
10 4.6692
11 4.6692
12 4.6692
13 4.66921</pre>
 
=={{header|Modula-2}}==
<langsyntaxhighlight lang="modula2">MODULE Feigenbaum;
FROM FormatString IMPORT FormatString;
FROM LongStr IMPORT RealToStr;
Line 880 ⟶ 1,525:
 
ReadChar
END Feigenbaum.</langsyntaxhighlight>
 
=={{header|Nim}}==
{{trans|Kotlin}}
<syntaxhighlight lang="nim">import strformat
 
iterator feigenbaum(): tuple[n: int; δ: float] =
## Yield successive approximations of Feigenbaum constant.
 
const
MaxI = 13
MaxJ = 10
var
a1 = 1.0
a2 = 0.0
δ = 3.2
 
for i in 2..MaxI:
var a = a1 + (a1 - a2) / δ
for j in 1..MaxJ:
var x, y = 0.0
for _ in 1..(1 shl i):
y = 1 - 2 * y * x
x = a - x * x
a -= x / y
 
δ = (a1 - a2) / (a - a1)
a2 = a1
a1 = a
yield (i, δ)
 
echo " i δ"
for n, δ in feigenbaum():
echo fmt"{n:2d} {δ:.8f}"</syntaxhighlight>
 
{{out}}
<pre> i δ
2 3.21851142
3 4.38567760
4 4.60094928
5 4.65513050
6 4.66611195
7 4.66854858
8 4.66906066
9 4.66917155
10 4.66919515
11 4.66920026
12 4.66920098
13 4.66920537</pre>
 
=={{header|Perl}}==
<langsyntaxhighlight lang="perl">use strict;
use warnings;
use Math::AnyNum 'sqr';
Line 908 ⟶ 1,601:
($a2, $a1) = ($a1, $a);
printf "%2d %17.14f\n", $i, $d1;
}</langsyntaxhighlight>
{{out}}
<pre> 2 3.21851142203809
Line 922 ⟶ 1,615:
12 4.66920131329420
13 4.66920154578091</pre>
 
=={{header|Perl 6}}==
{{works with|Rakudo|2018.04.01}}
{{trans|Ring}}
 
<lang perl6>my $a1 = 1;
my $a2 = 0;
my $d = 3.2;
 
say ' i d';
 
for 2 .. 13 -> $exp {
my $a = $a1 + ($a1 - $a2) / $d;
do {
my $x = 0;
my $y = 0;
for ^2 ** $exp {
$y = 1 - 2 * $y * $x;
$x = $a - $x²;
}
$a -= $x / $y;
} xx 10;
$d = ($a1 - $a2) / ($a - $a1);
($a2, $a1) = ($a1, $a);
printf "%2d %.8f\n", $exp, $d;
}</lang>
{{out}}
<pre> i d
2 3.21851142
3 4.38567760
4 4.60094928
5 4.65513050
6 4.66611195
7 4.66854858
8 4.66906066
9 4.66917155
10 4.66919515
11 4.66920026
12 4.66920098
13 4.66920537</pre>
 
=={{header|Phix}}==
{{trans|Ring}}
<!--<syntaxhighlight lang="phix">(phixonline)-->
<lang Phix>constant maxIt = 13,
<span style="color: #008080;">constant</span> <span style="color: #000000;">maxIt</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">13</span><span style="color: #0000FF;">,</span>
maxItJ = 10
<span style="color: #000000;">maxItJ</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">10</span>
atom a1 = 1.0,
<span style="color: #004080;">atom</span> <span style="color: #000000;">a1</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1.0</span><span style="color: #0000FF;">,</span>
a2 = 0.0,
<span style="color: #000000;">a2</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0.0</span><span style="color: #0000FF;">,</span>
d1 = 3.2
<span style="color: #000000;">d1</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">3.2</span>
puts(1," i d\n")
<span style="color: #7060A8;">puts</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" i d\n"</span><span style="color: #0000FF;">)</span>
for i=2 to maxIt do
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #000000;">maxIt</span> <span style="color: #008080;">do</span>
atom a = a1 + (a1 - a2) / d1
<span style="color: #004080;">atom</span> <span style="color: #000000;">a</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">a1</span> <span style="color: #0000FF;">+</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">a1</span> <span style="color: #0000FF;">-</span> <span style="color: #000000;">a2</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">/</span> <span style="color: #000000;">d1</span>
for j=1 to maxItJ do
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">maxItJ</span> <span style="color: #008080;">do</span>
atom x = 0, y = 0
<span style="color: #004080;">atom</span> <span style="color: #000000;">x</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">y</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
for k=1 to power(2,i) do
<span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
y = 1 - 2*y*x
<span style="color: #000000;">y</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span> <span style="color: #0000FF;">-</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">*</span><span style="color: #000000;">y</span><span style="color: #0000FF;">*</span><span style="color: #000000;">x</span>
x = a - x*x
<span style="color: #000000;">x</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">a</span> <span style="color: #0000FF;">-</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">*</span><span style="color: #000000;">x</span>
end for
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
a = a - x/y
<span style="color: #000000;">a</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">a</span> <span style="color: #0000FF;">-</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">/</span><span style="color: #000000;">y</span>
end for
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
atom d = (a1-a2)/(a-a1)
<span style="color: #004080;">atom</span> <span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">a1</span><span style="color: #0000FF;">-</span><span style="color: #000000;">a2</span><span style="color: #0000FF;">)/(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">-</span><span style="color: #000000;">a1</span><span style="color: #0000FF;">)</span>
printf(1,"%2d %.8f\n",{i,d})
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%2d %.8f\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">d</span><span style="color: #0000FF;">})</span>
d1 = d
<span style="color: #000000;">d1</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">d</span>
a2 = a1
<span style="color: #000000;">a2</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">a1</span>
a1 = a
<span style="color: #000000;">a1</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">a</span>
end for</lang>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<!--</syntaxhighlight>-->
{{out}}
<pre>
Line 1,006 ⟶ 1,661:
=={{header|Python}}==
{{trans|D}}
<langsyntaxhighlight lang="python">max_it = 13
max_it_j = 10
a1 = 1.0
Line 1,027 ⟶ 1,682:
d1 = d
a2 = a1
a1 = a</langsyntaxhighlight>
{{out}}
<pre> i d
Line 1,045 ⟶ 1,700:
=={{header|Racket}}==
{{trans|C}}
<langsyntaxhighlight lang="racket">#lang racket
(define (feigenbaum #:max-it (max-it 13) #:max-it-j (max-it-j 10))
(displayln " i d" (current-error-port))
Line 1,064 ⟶ 1,719:
 
(module+ main
(feigenbaum))</langsyntaxhighlight>
{{out}}
<pre> i d
Line 1,080 ⟶ 1,735:
13 4.66920537
4.669205372040318</pre>
 
=={{header|Raku}}==
(formerly Perl 6)
{{works with|Rakudo|2018.04.01}}
{{trans|Ring}}
 
<syntaxhighlight lang="raku" line>my $a1 = 1;
my $a2 = 0;
my $d = 3.2;
 
say ' i d';
 
for 2 .. 13 -> $exp {
my $a = $a1 + ($a1 - $a2) / $d;
do {
my $x = 0;
my $y = 0;
for ^2 ** $exp {
$y = 1 - 2 * $y * $x;
$x = $a - $x²;
}
$a -= $x / $y;
} xx 10;
$d = ($a1 - $a2) / ($a - $a1);
($a2, $a1) = ($a1, $a);
printf "%2d %.8f\n", $exp, $d;
}</syntaxhighlight>
{{out}}
<pre> i d
2 3.21851142
3 4.38567760
4 4.60094928
5 4.65513050
6 4.66611195
7 4.66854858
8 4.66906066
9 4.66917155
10 4.66919515
11 4.66920026
12 4.66920098
13 4.66920537</pre>
 
=={{header|REXX}}==
{{trans|Sidef}}
<langsyntaxhighlight lang="rexx">/*REXX pgm calculates the (Mitchell) Feigenbaum bifurcation velocity, #digs can be given*/
parse arg digs maxi maxj . /*obtain optional argument from the CL.*/
if digs=='' | digs=="," then digs= 30 /*Not specified? Then use the default.*/
Line 1,089 ⟶ 1,785:
if maxJ=='' | maxJ=="," then maxJ= 10 /* " " " " " " */
#= 4.669201609102990671853203820466201617258185577475768632745651343004134330211314737138,
|| 68974402394801381716 || 68974402394801381716 /*◄──Feigenbaum's constant, true value.*/
numeric digits digs /*use the specified # of decimal digits*/
a1= 1
Line 1,096 ⟶ 1,792:
say 'Using ' maxJ " iterations for maxJ, with " digs ' decimal digits:'
say
say copies(' ', 9) center('"correct'", 11) copies(' ', digs+1)
say center('i', 9, "─") center('digits' , 11, '"'") center('d', digs+1, "─")
 
do i=2 for maxi-1
Line 1,113 ⟶ 1,809:
parse value d a1 a with d1 a2 a1 /*assign 3 variables with 3 new values.*/
end /*i*/
say /*stick a fork in it, we're all done. */
say left('', 9 + 1 + 11 + 1 + truet value= ' # / 1)"↑" /*trueshow valueposition of Feigenbaum'sgreatest constantaccuracy. */</lang>
say ' true value= ' # / 1 /*true value of Feigenbaum's constant. */</syntaxhighlight>
{{out|output|text=&nbsp; when using the default inputs:}}
<pre>
Line 1,140 ⟶ 1,837:
19 10 4.66920160909687888294310165196
20 12 4.66920160910169069039564432665
 
true value= 4.66920160910299067185320382047
</pre>
 
=={{header|Ring}}==
<langsyntaxhighlight lang="ring"># Project : Feigenbaum constant calculation
 
decimals(8)
Line 1,175 ⟶ 1,872:
a2 = a1
a1 = a
next</langsyntaxhighlight>
Output:
<pre>Feigenbaum constant calculation:
Line 1,191 ⟶ 1,888:
12 4.66920098
13 4.66920537</pre>
 
=={{header|RPL}}==
{{trans|Python}}
{{works with|Halcyon Calc|4.2.7}}
{| class="wikitable"
! RPL code
! Python code
|-
|
≪ { }
13 10 → maxit maxitj
≪ 3.2 1 0
2 maxit 1 + '''FOR''' ii
DUP2 - 4 PICK / 3 PICK +
1 maxitj 1 + '''START'''
0 0
1 2 ii ^ '''START'''
OVER * 2 * 1 SWAP -
3 PICK ROT SQ - SWAP '''NEXT'''
/ - '''NEXT'''
3 PICK ROT - OVER 4 PICK - /
5 ROLL OVER + 5 ROLLD
4 ROLL DROP SWAP ROT '''NEXT'''
3 DROPN
≫ ≫
´'''FBAUM'''’ STO
|
'''FBAUM''' ''( -- { δ1..δ13 } )''
max_it, max_it_j = 13, 10
d1, a1, a2 = 3.2, 1, 0
for i in range(2, max_it + 1):
a = a1 + (a1 - a2) / d1
for j in range(1, max_it_j + 1):
x = y = 0
for k in range(1, (1 << i) + 1):
y = 1.0 - 2.0 * y * x
x = a - x * x
a = a - x / y
d = (a1 - a2) / (a - a1)
print(d)
d1, a2, a1 = d, a1, a
clean stack
.
.
|}
{{out}}
<pre>
1: { 3.21851142204 4.38567759857 4.60094927654 4.65513049539 4.66611194782 4.66854858152 4.66906066029 4.66917155686 4.6691951528 4.66920033694 4.66920090912 4.66920429563 4.66917851362 }
</pre>
The above program (limited at 10 iterations) takes 33 minutes and 50 seconds to be executed on a HP-28S.
 
=={{header|Ruby}}==
{{trans|C#}}
<syntaxhighlight lang="ruby">def main
maxIt = 13
maxItJ = 10
a1 = 1.0
a2 = 0.0
d1 = 3.2
puts " i d"
for i in 2 .. maxIt
a = a1 + (a1 - a2) / d1
for j in 1 .. maxItJ
x = 0.0
y = 0.0
for k in 1 .. 1 << i
y = 1.0 - 2.0 * y * x
x = a - x * x
end
a = a - x / y
end
d = (a1 - a2) / (a - a1)
print "%2d %.8f\n" % [i, d]
d1 = d
a2 = a1
a1 = a
end
end
 
main()</syntaxhighlight>
{{out}}
<pre> i d
2 3.21851142
3 4.38567760
4 4.60094928
5 4.65513050
6 4.66611195
7 4.66854858
8 4.66906066
9 4.66917155
10 4.66919515
11 4.66920026
12 4.66920098
13 4.66920537</pre>
 
=={{header|Scala}}==
===Imperative, ugly===
<langsyntaxhighlight Scalalang="scala">object Feigenbaum1 extends App {
val (max_it, max_it_j) = (13, 10)
var (a1, a2, d1, a) = (1.0, 0.0, 3.2, 0.0)
Line 1,217 ⟶ 2,009:
}
 
}</langsyntaxhighlight>
===Functional Style, Tail recursive===
{{Out}}Best seen running in your browser either by [https://scalafiddle.io/sf/OjA3sae/0 ScalaFiddle (ES aka JavaScript, non JVM)] or [https://scastie.scala-lang.org/04eS3BfCShmrA7I8ZmQfJA Scastie (remote JVM)].
<langsyntaxhighlight Scalalang="scala">object Feigenbaum2 extends App {
private val (max_it, max_it_j) = (13, 10)
 
Line 1,253 ⟶ 2,045:
result.foreach { case (δ, i) => println(f"${i + 2}%2d $δ%.8f") }
 
}</langsyntaxhighlight>
 
=={{header|Sidef}}==
{{trans|Perl 6Raku}}
<langsyntaxhighlight lang="ruby">var a1 = 1
var a2 = 0
var δ = 3.2.float
Line 1,276 ⟶ 2,068:
(a2, a1) = (a1, a0)
printf("%2d %.8f\n", i, δ)
}</langsyntaxhighlight>
{{out}}
<pre>
Line 1,300 ⟶ 2,092:
{{trans|C}}
 
<langsyntaxhighlight lang="swift">import Foundation
 
func feigenbaum(iterations: Int = 13) {
Line 1,334 ⟶ 2,126:
}
 
feigenbaum()</langsyntaxhighlight>
 
{{out}}
Line 1,354 ⟶ 2,146:
=={{header|Visual Basic .NET}}==
{{trans|C#}}
<langsyntaxhighlight lang="vbnet">Module Module1
 
Sub Main()
Line 1,382 ⟶ 2,174:
End Sub
 
End Module</langsyntaxhighlight>
{{out}}
<pre> i d
Line 1,397 ⟶ 2,189:
12 4.66920098
13 4.66920537</pre>
 
=={{header|V (Vlang)}}==
{{trans|Go}}
<syntaxhighlight lang="v (vlang)">fn feigenbaum() {
max_it, max_itj := 13, 10
mut a1, mut a2, mut d1 := 1.0, 0.0, 3.2
println(" i d")
for i := 2; i <= max_it; i++ {
mut a := a1 + (a1-a2)/d1
for j := 1; j <= max_itj; j++ {
mut x, mut y := 0.0, 0.0
for k := 1; k <= 1<<u32(i); k++ {
y = 1.0 - 2.0*y*x
x = a - x*x
}
a -= x / y
}
d := (a1 - a2) / (a - a1)
println("${i:2} ${d:.8f}")
d1, a2, a1 = d, a1, a
}
}
fn main() {
feigenbaum()
}</syntaxhighlight>
 
{{out}}
<pre>
i d
2 3.21851142
3 4.38567760
4 4.60094928
5 4.65513050
6 4.66611195
7 4.66854858
8 4.66906066
9 4.66917155
10 4.66919515
11 4.66920026
12 4.66920098
13 4.66920537
</pre>
 
=={{header|Wren}}==
{{trans|Ring}}
{{libheader|Wren-fmt}}
<syntaxhighlight lang="wren">import "./fmt" for Fmt
 
var feigenbaum = Fn.new {
var maxIt = 13
var maxItJ = 10
var a1 = 1
var a2 = 0
var d1 = 3.2
System.print(" i d")
for (i in 2..maxIt) {
var a = a1 + (a1 - a2)/d1
for (j in 1..maxItJ) {
var x = 0
var y = 0
for (k in 1..(1<<i)) {
y = 1 - 2*y*x
x = a - x*x
}
a = a - x/y
}
var d = (a1 - a2)/(a - a1)
System.print("%(Fmt.d(2, i)) %(Fmt.f(0, d, 8))")
d1 = d
a2 = a1
a1 = a
}
}
 
feigenbaum.call()</syntaxhighlight>
 
{{out}}
<pre>
i d
2 3.21851142
3 4.38567760
4 4.60094928
5 4.65513050
6 4.66611195
7 4.66854858
8 4.66906066
9 4.66917155
10 4.66919515
11 4.66920026
12 4.66920098
13 4.66920537
</pre>
 
=={{header|XPL0}}==
{{trans|Wren}}
<syntaxhighlight lang "XPL0">def MaxIt = 13, MaxItJ = 10;
real A, A1, A2, D, D1, X, Y;
int I, J, K;
[A1:= 1.; A2:= 0.; D1:= 3.2;
Text(0, " i d^m^j");
for I:= 2 to MaxIt do
[A:= A1 + (A1-A2)/D1;
for J:= 1 to MaxItJ do
[X:= 0.; Y:= 0.;
for K:= 1 to 1<<I do
[Y:= 1. - 2.*Y*X;
X:= A - X*X;
];
A:= A - X/Y;
];
D:= (A1-A2) / (A-A1);
Format(2, 0); RlOut(0, float(I));
Format(5, 8); RlOut(0, D);
CrLf(0);
D1:= D;
A2:= A1;
A1:= A;
];
]</syntaxhighlight>
{{out}}
<pre>
i d
2 3.21851142
3 4.38567760
4 4.60094928
5 4.65513050
6 4.66611195
7 4.66854858
8 4.66906066
9 4.66917155
10 4.66919515
11 4.66920026
12 4.66920098
13 4.66920537
</pre>
 
=={{header|zkl}}==
{{trans|Kotlin}}
<langsyntaxhighlight lang="zkl">fcn feigenbaum{
maxIt,maxItJ,a1,a2,d1,a,d := 13, 10, 1.0, 0.0, 3.2, 0, 0;
println(" i d");
Line 1,414 ⟶ 2,342:
d1,a2,a1 = d,a1,a;
}
}();</langsyntaxhighlight>
{{out}}
<pre>
1,972

edits