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Have 2D-fractals-giving CAs rules 2 "variables"?

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Have 2D-fractals-giving CAs rules 2 "variables"?

Postby Koiti Kimura » October 19th, 2017, 1:39 am

1. Do all the conjunctions of the CAs rules generating or representing two-dimensional self-similar fractals have two "variables"/factors (including a parameter) as in the recurrence formula producing or representing the Mandelbrot set coupled with the Julia set(s)?
2. And do all the functions/maps generating or representing 2D self-similar fractals possess double periodicities like that of the Mandelbrot set coupled with the Julia set(s)? I mean, the self-similarity periodicity (repetitive appearances of self-similar parts) of the Mandelbrot set plus the self-similarity periodicity (ditto) of the Julia set(s). In other words, are all the functions/maps for self-similar fractals doubly-periodic?
Koiti Kimura
 
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