06
Jul
09

3D Exponential Mandelbrot Set

This is what the Mandelbrot set looks like if you vary the exponent along the third dimension. It has a twisted shape because the features of the Mandelbrot set rotate as the exponent is increased. Technically, this is not a hypercomplex fractal, but it’s still worth mentioning here.

Here is some Mathematica code:
(* runtime: 49 seconds, increase n for higher resolution *)
n = 100; Mandelbrot[n_, zc_] := Module[{z = 0, i = 0}, While[i <12 && Abs[z] < 2, z = z^n + zc; i++]; i];
image = Table[y = 1.5; While[y >= 0 && Mandelbrot[z, x + I y] < 12, y -= 3/n]; y, {z, 1, 4, 3/n}, {x, -2, 1, 3/n}];
ListDensityPlot[image, Mesh -> False, Frame -> False, PlotRange -> {0, 1.5}]

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