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First you must understand the difference between machine precision arithmetic (CPU floating point) and Mathematica's own arbitrary precision arithmetic. You get the first by calling N with one argument and the second by calling N with two arguments, the second being the precision you want to maintain. When using Mathematica's own arbitrary precision ...


Incidentally, here is a higher resolution picture of the image produced by heropup's answer, plotted over both positive and negative values of the two circle map parameters: Blue represents negative, yellow represents positive. You can view a far larger 6001x6001 pixel image (about 29MB) here. Here is the code used to generate the upper right quarter of ...

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