Dépêche Math Mandelbrot sequence f (z) 0; fₙ (z) (fₙ(z)) + z

Animated development of the Mandelbrot sequence f(z) 0; fₙ(z) (fₙ(z)) + z with some mathematical annotations and explanations. See xxx for a version without mathematical subtitles. Music: Doug Maxwell, Cast of Pods This animation covers the recursively defined sequence of polynomials f(z) 0; fₙ(z) (fₙ(z)) + z which is closely related to the famous Mandelbrot fractal set. Its development is depicted by coloring the points of the complex plane according to the values of fₙ(z). See legend in the lower left corner for how to translate these colors to complex values. Speaking in terms of dynamical systems theory, we discuss this recursion not in the dynamic plane but rather in the parameter plane and study the sequence members as functions of this parameter. Animation imaging was created using CPV, a program written by myself for visualizing complex functions, developed within Lazarus IDE. Watch video in Full HD resolution (1080p) and full screen mode for best viewing experience.