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Author Topic: *Continued* SuperFractalThing: Arbitrary precision mandelbrot set rendering in Java.  (Read 13453 times)
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therror
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« Reply #345 on: September 23, 2017, 09:10:09 AM »

Hi! How to find coefficients A[k] for Multibrot arbitrary integer power? Does exist generalization of formula in http://mathr.co.uk/blog/2016-03-06_simpler_series_approximation.html ? Thanks )
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claude
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« Reply #346 on: September 24, 2017, 07:29:36 PM »

Hi! How to find coefficients A[k] for Multibrot arbitrary integer power? Does exist generalization of formula in http://mathr.co.uk/blog/2016-03-06_simpler_series_approximation.html ? Thanks )

I asked on M.SE, which shows how to get the equations for the A[k], just not in an explicit recursion (you have to expand the power series and collect terms):
https://math.stackexchange.com/questions/2443377/closed-form-for-these-power-series-coefficients
The equations for the A[k] coefficients are defined implicitly, don't know an explicit closed form solution.  The implicit form may be enough, depending what you need to do.
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claude
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« Reply #347 on: September 28, 2017, 10:20:19 PM »

I answered my own M.SE question, with Maxima source code that can be used (with only a little extra manual work) to get the explicit recursion formula for a specific P.

The problem for arbitrary P is that (in code terms) you'd need nested loops to a depth of P-1, and most programming languages don't let you do that easily.
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