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This is always a challenge for me to determine the maximum number of iteration for Mandelbrot set.

If you specify the region, it is fine. I can find the best maximum iteration by trial and error.

But the problem rises when I need a general case formula/algorithm to determine the maximum iteration no matter where I zoom.

A very low maximum iteration leads to loss of details and sometimes you cannot zoom anymore as all colors become the same.

A very high maximum iteration will lead to a high computational time as well as too distractive details.

Another point is I prefer an algorithm/formula that gives me a continuous result when I keep zooming. I don't like my colors suddenly jump dramatically.

Ideally, it is better to avoid calculation of Mandelbrot multiple times to realize the best maximum iteration.

Is there any known solution for setting the maximum iteration for Mandelbrot set?

maximum iteration

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So you are looking for the Automatic Dwell Limit algorithms

Remember also about updating precision with zoom

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  • $\begingroup$ This isn't an answer $\endgroup$
    – eric
    Dec 17, 2023 at 18:30

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