These are the materials, mainly jupyter notebook, of the course I taught at the School of Molecular and Theoretical Biology the summer of 2016 in Barcelona on Complex Dynamical Systems and Python.
Complex dynamical systems have been studied for over one-hundred years and there are still notable open conjectures. Yet, to have a basic understanding of the rules of the game it only requires basic understanding of complex numbers and recursive functions. This course combines theory lessons with practical work using Jupyter Notebooks. The notebooks contain explanations and exercises.
Julia sets of the polynomial f(z)=z^2 - 0.8 - 0.15i. Repeated iterations of this function on different values in the complex plane lead to different behaviours. The Julia set (vs Fatou set) consists of the points where the behavior is chaotic (vs regular).
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The Mandelbrot Set is a map of Julia Sets. More concretely, the coloring of a point c measures properties of the Julia set of the polynomial z^2 + c.
