This web content explores the beauty and complexity of the Mandelbrot set, focusing on a perturbation technique introduced by K.I. Martin in 2013. The technique allows for more efficient iteration of complex fractals, such as the Mandelbrot set and the Burning Ship fractal, by using high precision reference orbits and low precision perturbed orbits to compute differences. The content covers the challenges of perturbation glitches, rescaling for deep zooms, and extending the technique to hybrid fractals. It also discusses series approximation methods to skip iterations and speed up calculations, with ongoing research on applying these techniques to chains of minibrots for further efficiency.
https://mathr.co.uk/blog/2021-05-14_deep_zoom_theory_and_practice.html