Deep Zooming into the Mandelbrot Set: Theory and Practice
2025-01-03
This article delves into the theory and practice of deep zooming into the Mandelbrot set. Traditional algorithms for rendering the Mandelbrot set are computationally expensive. The author introduces acceleration techniques based on perturbation theory, including perturbation iterations, glitch detection, and rescaling. Furthermore, the article discusses series approximation techniques and how to handle challenges such as "deep needle" regions and hybrid fractals. These optimizations drastically improve rendering speed, enabling the creation of more detailed images.