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# Mandelbrot visualisation

Matthen Jun 18th, 2013 330 Never
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1. f21 = Compile[{{n, _Real}, {x, _Real}, {y, _Real}}, Re[
2.     With[{f =
3.        Nest[If[Abs[#] <= 100, (#^2 + x + I y), #] &, 0, Floor[n]],
4.       t = n - Floor[n]},
5.      f (1 - t) + (f^2 + x + I y) (t)
6.      ]
7.
8.     ], CompilationTarget -> "C"];
9. f22 = Compile[{{n, _Real}, {x, _Real}, {y, _Real}},
10.    Im[
11.     With[{f =
12.        Nest[If[Abs[#] <= 100, (#^2 + x + I y), #] &, 0, Floor[n]],
13.       t = n - Floor[n]},
14.      f (1 - t) + (f^2 + x + I y) (t)
15.      ]
16.     ]
17.    , CompilationTarget -> "C"];
18.
19. img0 = Rasterize[Graphics[
20.     Table[
21.      {ColorData["DarkRainbow"][r], Disk[{0, 0}, 1 - r]}
22.      , {r, 0, 1, 0.04}]
23.     , Background -> Black], RasterSize -> 200, ImageSize -> 200];
24.
25. frame[n_] := ImageTransformation[img0,
26.    Function[{p}, With[{x = p[[1]], y = p[[2]]},
27.      {f21[n, x, y], f22[n, x, y]}
28.      ]
29.     ]
30.    , DataRange -> {{-2, 1}, {-1.5, 1.5}}];
31. frames = Table[frame[n^2], {n, 1, 3.5, 2.5/87}];
32. Export["mandel.gif", frames]
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