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
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
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
- Date : 2018/04/20
- Author : Gal Zsolt [~ CalmoSoft ~]
- Email : <calmosoft@gmail.com>
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
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