Feigenbaum constant calculation
Feigenbaum constant calculation is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
Calculate the Feigenbaum constant. See details: Feigenbaum constant
C
<lang c>#include <stdio.h>
void feigenbaum() {
int i, j, k, max_it = 13, max_it_j = 10;
double a, x, y, d, a1 = 1.0, a2 = 0.0, d1 = 3.2;
printf(" i d\n");
for (i = 2; i <= max_it; ++i) {
a = a1 + (a1 - a2) / d1;
for (j = 1; j <= max_it_j; ++j) {
x = 0.0;
y = 0.0;
for (k = 1; k <= 1 << i; ++k) {
y = 1.0 - 2.0 * y * x;
x = a - x * x;
}
a -= x / y;
}
d = (a1 - a2) / (a - a1);
printf("%2d %.8f\n", i, d);
d1 = d;
a2 = a1;
a1 = a;
}
}
int main() {
feigenbaum(); return 0;
}</lang>
- Output:
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
C#
<lang csharp>using System;
namespace FeigenbaumConstant {
class Program {
static void Main(string[] args) {
var maxIt = 13;
var maxItJ = 10;
var a1 = 1.0;
var a2 = 0.0;
var d1 = 3.2;
Console.WriteLine(" i d");
for (int i = 2; i <= maxIt; i++) {
var a = a1 + (a1 - a2) / d1;
for (int j = 1; j <= maxItJ; j++) {
var x = 0.0;
var 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;
}
var d = (a1 - a2) / (a - a1);
Console.WriteLine("{0,2:d} {1:f8}", i, d);
d1 = d;
a2 = a1;
a1 = a;
}
}
}
}</lang>
- Output:
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
D
<lang d>import std.stdio;
void main() {
int max_it = 13; int max_it_j = 10; double a1 = 1.0; double a2 = 0.0; double d1 = 3.2; double a;
writeln(" i d");
for (int i=2; i<=max_it; i++) {
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);
writefln("%2d %.8f", i, d);
d1 = d;
a2 = a1;
a1 = a;
}
}</lang>
- Output:
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 4.66920028 12 4.66920099 13 4.66920555
Go
<lang go>package main
import "fmt"
func feigenbaum() {
maxIt, maxItJ := 13, 10
a1, a2, d1 := 1.0, 0.0, 3.2
fmt.Println(" i d")
for i := 2; i <= maxIt; i++ {
a := a1 + (a1-a2)/d1
for j := 1; j <= maxItJ; j++ {
x, y := 0.0, 0.0
for k := 1; k <= 1<<uint(i); k++ {
y = 1.0 - 2.0*y*x
x = a - x*x
}
a -= x / y
}
d := (a1 - a2) / (a - a1)
fmt.Printf("%2d %.8f\n", i, d)
d1, a2, a1 = d, a1, a
}
}
func main() {
feigenbaum()
}</lang>
- Output:
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
Haskell
<lang haskell>import Data.List (mapAccumL, foldl') --' strict
feigenbaumApprox :: Int -> [Double] feigenbaumApprox mx = snd $ mitch mx 10
where
mitch :: Int -> Int -> ((Double, Double, Double), [Double])
mitch mx mxj =
mapAccumL
(\(a1, a2, d1) i ->
let a =
foldl' --' strict variant of foldl
(\acc _ ->
let (x, y) =
iterate
(\(p, q) ->
(acc - (p * p), 1.0 - ((2.0 * p) * q)))
(0.0, 0.0) !!
(2 ^ i)
in acc - (x / y))
(a1 + (a1 - a2) / d1)
[1 .. mxj]
d = (a1 - a2) / (a - a1)
in ((a, a1, d), d))
(1.0, 0.0, 3.2)
(take mx [2 ..])
main :: IO () main =
(putStrLn . unlines) $ zipWith (\i s -> justifyRight 2 ' ' (show i) ++ '\t' : s) [1 ..] (show <$> feigenbaumApprox 13) where justifyRight n c s = drop (length s) (replicate n c ++ s)</lang>
- Output:
1 3.2185114220380866 2 4.3856775985683365 3 4.600949276538056 4 4.6551304953919646 5 4.666111947822846 6 4.668548581451485 7 4.66906066077106 8 4.669171554514976 9 4.669195154039278 10 4.669200256503637 11 4.669200975097843 12 4.669205372040318 13 4.669207514010413
Kotlin
<lang scala>// Version 1.2.40
fun feigenbaum() {
val maxIt = 13
val maxItJ = 10
var a1 = 1.0
var a2 = 0.0
var d1 = 3.2
println(" i d")
for (i in 2..maxIt) {
var a = a1 + (a1 - a2) / d1
for (j in 1..maxItJ) {
var x = 0.0
var y = 0.0
for (k in 1..(1 shl i)) {
y = 1.0 - 2.0 * y * x
x = a - x * x
}
a -= x / y
}
val d = (a1 - a2) / (a - a1)
println("%2d %.8f".format(i,d))
d1 = d
a2 = a1
a1 = a
}
}
fun main(args: Array<String>) {
feigenbaum()
}</lang>
- Output:
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
Modula-2
<lang modula2>MODULE Feigenbaum; FROM FormatString IMPORT FormatString; FROM LongStr IMPORT RealToStr; FROM Terminal IMPORT WriteString,WriteLn,ReadChar;
VAR
buf : ARRAY[0..63] OF CHAR; i,j,k,max_it,max_it_j : INTEGER; a,x,y,d,a1,a2,d1 : LONGREAL;
BEGIN
max_it := 13; max_it_j := 10;
a1 := 1.0; a2 := 0.0; d1 := 3.2;
WriteString(" i d");
WriteLn;
FOR i:=2 TO max_it DO
a := a1 + (a1 - a2) / d1;
FOR j:=1 TO max_it_j DO
x := 0.0;
y := 0.0;
FOR k:=1 TO INT(1 SHL i) DO
y := 1.0 - 2.0 * y * x;
x := a - x * x
END;
a := a - x / y
END;
d := (a1 - a2) / (a - a1);
FormatString("%2i ", buf, i);
WriteString(buf);
RealToStr(d, buf);
WriteString(buf);
WriteLn;
d1 := d;
a2 := a1;
a1 := a
END;
ReadChar
END Feigenbaum.</lang>
Perl 6
<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>
- Output:
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
Phix
<lang Phix>constant maxIt = 13,
maxItJ = 10
atom a1 = 1.0,
a2 = 0.0,
d1 = 3.2
puts(1," i d\n") for i=2 to maxIt do
atom a = a1 + (a1 - a2) / d1
for j=1 to maxItJ do
atom x = 0, y = 0
for k=1 to power(2,i) do
y = 1 - 2*y*x
x = a - x*x
end for
a = a - x/y
end for
atom d = (a1-a2)/(a-a1)
printf(1,"%2d %.8f\n",{i,d})
d1 = d
a2 = a1
a1 = a
end for</lang>
- Output:
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
Racket
<lang racket>#lang racket (define (feigenbaum #:max-it (max-it 13) #:max-it-j (max-it-j 10))
(displayln " i d" (current-error-port))
(define-values (_a _a1 d)
(for/fold ((a 1) (a1 0) (d 3.2))
((i (in-range 2 (add1 max-it))))
(let* ((a′ (for/fold ((a (+ a (/ (- a a1) d))))
((j (in-range max-it-j)))
(let-values (([x y] (for/fold ((x 0) (y 0))
((k (expt 2 i)))
(values (- a (* x x))
(- 1 (* 2 y x))))))
(- a (/ x y)))))
(d′ (/ (- a a1) (- a′ a))))
(eprintf "~a ~a\n" (~a i #:width 2) (real->decimal-string d′ 8))
(values a′ a d′))))
d)
(module+ main
(feigenbaum))</lang>
- Output:
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 4.669205372040318
Ring
<lang ring>
- Project : Feigenbaum constant calculation
decimals(8) see "Feigenbaum constant calculation:" + nl maxIt = 13 maxItJ = 10 a1 = 1.0 a2 = 0.0 d1 = 3.2 see "i " + "d" + nl for i = 2 to maxIt
a = a1 + (a1 - a2) / d1
for j = 1 to maxItJ
x = 0
y = 0
for k = 1 to pow(2,i)
y = 1 - 2 * y * x
x = a - x * x
next
a = a - x / y
next
d = (a1 - a2) / (a - a1)
if i < 10
see "" + i + " " + d + nl
else
see "" + i + " " + d + nl
ok
d1 = d
a2 = a1
a1 = a
next </lang> Output:
Feigenbaum constant calculation: 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
Sidef
<lang ruby>var a1 = 1 var a2 = 0 var δ = 3.2.float
say " i\tδ"
for i in (2..15) {
var a0 = ((a1 - a2)/δ + a1)
10.times {
var (x, y) = (0, 0)
2**i -> times {
y = (1 - 2*x*y)
x = (a0 - x²)
}
a0 -= x/y
}
δ = ((a1 - a2) / (a0 - a1))
(a2, a1) = (a1, a0)
printf("%2d %.8f\n", i, δ)
}</lang>
- Output:
i δ 2 3.21851142 3 4.38567760 4 4.60094928 5 4.65513050 6 4.66611195 7 4.66854858 8 4.66906066 9 4.66917156 10 4.66919516 11 4.66920023 12 4.66920131 13 4.66920155 14 4.66920160 15 4.66920161
zkl
<lang zkl>fcn feigenbaum{
maxIt,maxItJ,a1,a2,d1,a,d := 13, 10, 1.0, 0.0, 3.2, 0, 0;
println(" i d");
foreach i in ([2..maxIt]){
a=a1 + (a1 - a2)/d1;
foreach j in ([1..maxItJ]){
x,y := 0.0, 0.0;
foreach k in ([1..(1).shiftLeft(i)]){ y,x = 1.0 - 2.0*y*x, a - x*x; } a-=x/y
}
d=(a1 - a2)/(a - a1);
println("%2d %.8f".fmt(i,d));
d1,a2,a1 = d,a1,a;
}
}();</lang>
- Output:
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