The author needs to learn about techniques for rendering deep zooms into the Mandelbrot set. Since 2013 it has been possible to render images that are 2^-hundreds across using mostly double precision arithmetic, apart from a few anchor points calculated with multiprecision (hundreds of bits) arithmetic.
The deep zoom mathematics includes techniques for introspecting the iterations to detect glitches, which need extra multiprecision anchor points to be calculated.
https://mathr.co.uk/blog/2021-05-14_deep_zoom_theory_and_pra...
https://dirkwhoffmann.github.io/DeepDrill/docs/Theory/Mandel...
In my experience of non-deep-zoom rendering, and contrary to the authors arguments, period detection works well for speeding up renders. It appeared to be fairly safe from false positives. https://dotat.at/@/2010-11-16-interior-iteration-with-less-p... https://dotat.at/prog/mandelbrot/cyclic.png