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One way of coding the iterations may be defined as follows. The function CollatzFractal01[z0] returns a list {Abs[z],iter}, where Abs[z] is the final value of z, and iter is the number of iterations required to escape the bound of Abs[z]>200. Use compilation and parallelisation for speed. CollatzFractal01 = Compile[{{z0, _Complex, 0}}, Module[{iter = ...

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