I'd like to get fractals out of these functions:
What I got now looks like this (for one of the equations), and though it can be used to generate some pretty pictures it isn't quite what I want (need). What I would like to see is something like this: Julia Set -- from Wolfram MathWorld
Code:
collatz = Compile[{{z, _Complex}},
Module[{x = z, i = 0, s = 10.^5, vic = 10.^5 + 0.0 I, maxit = 100},
While[i < maxit && Abs[x] < s, i++;
x = 1/4 (2 + 7 x - (2 + 5 x) Cos[\[Pi] x]);
If[Abs[x] < Abs[vic], vic = Abs[x], vic];]; vic]]
sol = Table[
collatz[x + I y], {x, 1.5, 2.5, .003}, {y, -0.5, 0.5, .003}] // Chop;
ListDensityPlot[sol, Mesh -> False, ColorFunction -> (Hue)]
Any help would be highly appreciated.