Sujet

Correction en OCaml

Exercice 1.

let add (r1, i1) (r2, i2) = (r1 +. r2, i1 +. i2)
let mult (r1, i1) (r2, i2) =
  ((r1 *. r2) -. (i1 *. i2), (r1 *. i2) +. (r2 *. i1))
let norme2 (r, i) = sqrt (r *. r +. i *. i)
      

Exercice 2

let limite_iteration = 50
let limite_norme2 = 4.

let divergence c =
  let rec iter i z_i =
    if i >= limite_iteration || norme2 z_i >= limite_norme2
    then i
    else iter (succ i) (add (mult z_i z_i) c)
  in iter 0 (0., 0.)
      

Exercice 3

#load "graphics.cma"

let gris n =
  let c = (255 * n) / limite_iteration in
  Graphics.rgb c c c

Exercice 4

let point (taille_x, taille_y) (x, y) =
  (float (2 * x) /. float taille_x -. 1.5,
   float (2 * y) /. float taille_y -. 1.)
      

Exercice 5

let mandelbrot taille_x taille_y =
  Graphics.open_graph (Printf.sprintf " %dx%d" taille_x taille_y);
  for i = 0 to taille_x - 1 do
    for j = 0 to taille_y - 1 do
      let () = Graphics.set_color
		 (gris (divergence (point (taille_x, taille_y) (i, j)))) in
      Graphics.plot i j
    done
  done;
  let _ = Graphics.read_key () in
  Graphics.close_graph ()

let () = mandelbrot 800 600