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Recusive Forms with Complex Numbers

The rational recursive forms gave very nice 2 dimensional picturs, but what happens if we try to generate 3 dimensional sets?

The sets demomstrated here are still partly based on precision errors. But that does not matter, cause if we grow precision still nice but of course different pictures will appear.

So first try: dim 1 = iterations, dims 2 and 3 a complex number

Let the starting values belong to the set of complex numbers and every new value wil be a complex number too.

Here some examples:

and here a movie, that we can see like figures like this realy look like.

A projection along the iteration axis (lets only jump in the complex plane)

Same pics as on top of page:

And again I see so many connections to interessting things! Galaxies, quarks and strings ;-) Generally: growth and developement processes. And the one and only question: How precise is god or our universal computer (the universe)?