I guess that only once in a lifetime a programmer get the opportunity to take a real old concept, rendering the Mandelbrot set, and make it not twice as fast, or 10 times as fast, but 100 times faster than the fastest commercial program.
The Mandelbrot set has engaged many skilled programmers to take the challenge to make programs that renders it as fast as possible during decades, since it has been around since the 80s.
The real challenge is that with the data types built in the hardware only allows zooming to around 1e13. Going deeper requires much slower software calculations - for each pixel!
Thanks to Perturbation and Series Approximation, high precision is needed only in one pixel that can be used as a reference and the rest of the pixels calculated with hardware data types.

More info can be found here:
en.wikipedia.org/wiki/Mandelbrot_set#Perturbation_…


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