Short implicit plot of Mandelbrot set using Misiurewicz polynomial /
Points:
( this seems to give more interior detail of potential lines than an
iterative method
and for the amount of detail is much faster as well)
Clear[f, g, h, x]
f[z_] = z2 + x
g = Join[{1}, ExpandAll[NestList[f, x, 5]]];
h = Union[Flatten[Table[Flatten[Table[If[n == m, {}, ExpandAll[g[[
n]] - g[[m]]]], {m, 1, n}]], {n, 1, Length[g]}]]];
k = Flatten[Table[If[Apply[Plus, CoefficientList[D[h[[n]], {x, 1}],
x]] == 0, {}, D[h[[n]], {x, 1}]], {n, 1, Length[h]}]]
Clear[x, y, a, b, f, z];
nr = k /. x -> z
p[z_] = Apply[Times, nr];
z = x + I*y;
f[x_, y_] = Re[1/(p[z])];
ContourPlot[ f[x,
y], {x, -2.4, 1}, {y, -1.7, 1.7},
PlotPoints -> {300, 300}, ImageSize ->
600, ColorFunction -> (Hue[2#] &)]
Respectfully, Roger L. Bagula
11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814
:http://www.geocities.com/rlbagulatftn/Index.html
alternative email: rlbagula@[EMAIL PROTECTED]
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