17
Jun
04

Newton-Raphson Fractal

f(z) = z5-1, zn+1 = zn – f(zn)/f'(zn)
It is surprisingly easy to make these beautiful fractals.

(* runtime: 1 minute *)
Show[Graphics[RasterArray[Table[Module[{data = FixedPointList[(4 # + 1/#^4)/5.0 &, x + I y, 29], z}, z = 1 - Length[data]/30; Hue[Arg[Last[data]]/(2Pi),Min[1, 2(1 - z)], Min[1, 2z]]], {x, -1.5, 1.5, 3.0/275}, {y, -1.5, 1.5, 3.0/275}]]], AspectRatio -> 1];

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