Yusheng Luo - Similarities and Non-Similarities in the Mandelbrot Set

The study of iterated complex polynomials dates back to the work of Fatou in the late 19th century and marks one of the earliest developments in dynamical systems. The process produces many beautiful fractal sets, with intricate and infinitely detailed structure. Among the most iconic ones is the Mandelbrot set. In this talk, I’ll explore why we see repeating patterns—self-similarities—within the Mandelbrot set, and explain why, despite their visual resemblance, these patterns are not truly the same in a geometric (conformal) sense.

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