La dinàmica dels polinomis complexos: The escaping set

Abstract

[en] In this project we study the dynamics of complex polynomials, leading towards an efficient algorithm to draw the relevant fractal objects that appear. First, we begin with a series of preliminary concepts necessary to be able to understand the properties of local and global theory, and then analyze the particular properties of polynomials. From here, we will delve into the quadratic family, specifically the Mandelbrot set. We develop Python code to visualize different sets of complex dynamics and see how the escaping and density algorithms work.