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Roger Bagulamovie of Generalized Cantor transformed Mandelbrot sets

Cantor pairs of the type {1/(p+1) ,p/(p+1)} are used to transform the Mandelbrot set in Mathematica.
Mathematica code:
Clear[f, x, k, nz, z, escapeCount, p]
(*sequential generalized Cantor set pretransform switch*)
(* a Cantor pair of {1/(p + 1), p/(p + 1)} : sum one : next p = 3*)
(* p + 1 = 4 gives at ratio of four *)
f[x_, k_] := If[Mod[k, 2] == 0, N[(x/(p + 1))^2],
N[(p*x/(p + 1) + p/(p + 1))^2]]
(* Bezier between p = 2 and p = 3*)
n = 20
p = 3*k/n + 1*(1 - k/n)
(*3D and plane Mandelbrots/ Julias *)
(*Mandelbrot with SQRT(x^2 + y^2) limited measure*)
(*by R. L. BAGULA 22. Nov 2007© © *)
numberOfz2ToEscape[z_] := Block[
{escapeCount, nz = N[z], nzold = 0},
For[
escapeCount = 0,
(Sqrt[Re[nz]^2 + Im[nz]^2] < 16) && (
escapeCount < 255) && (Abs[nz - nzold] > .5*10^(-3)),
nzold = nz;
nz = f[nz, escapeCount] + z;


++escapeCount
];
escapeCount
]
FractalPureM[{{ReMin_, ReMax_, ReSteps_},
{ImMin_, ImMax_, ImSteps_}}] :=
Table[
numberOfz2ToEscape[x + y I],
{y, ImMin, ImMax, (ImMax - ImMin)/ImSteps},
{x, ReMin, ReMax, (ReMax - ReMin)/ReSteps}

]

Table[ListDensityPlot[FractalPureM[{{-2*(p + 1)*2.5 + 2.5, 2.5, 100}, {-(
p + 1)*2.5, (p + 1)*2.5, 100}}],
Mesh -> False,
AspectRatio -> Automatic,
ColorFunction -> Hue];, {k, 0, 20}]


This movie is part of the collection: Open Source Movies

Producer: Roger Bagula
Keywords: Mandelbrot set; Cantor set; fractals ; animations; complex dynamics

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