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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