How to Find An Optimal Number of Maximum Iterations

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Byte11

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How to Find An Optimal Number of Maximum Iterations

« on: December 22, 2017, 12:13:52 AM »
I'm looking to find the optimal number of maximum iterations in the most computationally cheap way. I had a method where I would take a point (usually the center) and store it in full precision. Then I would limit the precision of the reference calculation to $$precision = frame + 15$$ with precision in bits (this is assuming magnification is given by 2^frame). Then I'd calculate the reference until the point tended towards 0 or infinity. The number of iterations that took would be the optimal number of iterations. However, this only worked given two things: 1. The point being calculated was relatively complex compared to the rest of the pixels 2. I had more bits of precision in my reference than I was using for my zooming.

This worked well if you take a point from a previous zoom and plug that into the formula. However, if the user is clicking on pixels and I convert those pixels to a new center point to use as a reference for this algorithm, the point is almost always unsuitable.

So I either need a way of finding points that fit the above criteria or another algorithm for finding an optimal number of iterations. For finding a suitable point, I was thinking to either use Misiurewicz points or Newton-Raphsoon zooming, but those are computationally expensive. Does anyone else have a better idea?

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Re: How to Find An Optimal Number of Maximum Iterations

« Reply #1 on: December 22, 2017, 01:25:13 AM »
in my mandelbrot-perturbator I do iterations in chunks: say 1000 reference iterations, then 1000 pixel iterations, repeat.  That way I mostly don't need to know the ideal maximum iteration count before starting, and can set it ludicrously high as it will stop when all pixels have escaped (the exception is when minibrots are visible, in which case some pixels would never escape - I will eventually extend mandelbrot-perturbator either to do interior checking or to keep doubling the iteration count until the rate of pixels escaping is low, a strategy I learned from Robert Munafo).

Adam Majewski

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Re: How to Find An Optimal Number of Maximum Iterations

« Reply #2 on: December 22, 2017, 04:02:03 PM »

Byte11

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Re: How to Find An Optimal Number of Maximum Iterations

« Reply #3 on: December 24, 2017, 01:26:47 AM »
The algorithm that I described above works well if the selected point is significantly deeper than the points in the viewing area but is still within the bounds of the viewing area. Is there a way to find points within the viewing area that are fairly deep that could be used for this algorithm?

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