Mokkosuでグモウスキー・ミラ写像を描画してみた

研究室の先輩が作ったプログラム言語Mokkosuで
グモウスキー・ミラ写像を描画するプログラムを作りました。

#スクリーンショット

#ソースコード

include "Graphics.mok";

#x(n+1) = y(n) + a(1-b y(n)^2)y(n) + f(x(n))
#y(n+1) = -x(n) + f(x(n+1))
#f(x) = mu x + 2(1-mu)x^2/(1+x^2)
let window_size = 500;
let x0 = 0.1;
let y0 = 0.1;
let a = 0.008;
let b = 0.05;
let mu = ~-.0.496;
let m = 11.5;

let iteration = 100000;

let calc_gumowski xpr ypr = 
  let f x = mu *. x +. 2.0 *. (1.0 -. mu)*. x *.x /. (1.0 +. x *. x) in
  let xn x y = y +. a *. (1.0 -. b *. y *. y)*.y +. (f x) in
  let yn x xn = ~-.x +. (f xn) in
  let x = xn xpr ypr in
  let y = yn xpr x in
  (x, y);  

let draw_gumowski gr =
  fun loop xpr ypr n =
    if n > iteration -> () else 
    let (x, y) = calc_gumowski xpr ypr in
    let distance = pow (x *. x +. y *. y) 0.5 *. m in
    let draw_x = double_to_int (x *. m) + window_size / 2 in
    let draw_y = double_to_int (y *. m) + window_size / 2 in
    let color_m =  distance /. (int_to_double (window_size / 2)) in
    let h = if color_m > 1.0 -> 360.0 else 360.0 *. color_m in
    let (r,g,b) = hsv_to_rgb h 0.6 0.9 in
    do draw_pixel gr r g b draw_x draw_y in
    loop  x y (n + 1)
  in
  loop x0 y0 1;
  
do scene "main" {
  ~Draw(gr) -> do
     draw_gumowski gr;
   end;
  _ -> ();
};

do set_size window_size window_size;

do show_window "main";