Dépêche Math Mandelbrot sequence f (z) 0; fₙ (z) (fₙ(z)) + z without subtitles

Animated development of the Mandelbrot sequence f(z) 0; fₙ(z) (fₙ(z)) + z without mathematical subtitles. See xxx for a version including mathematical remarks. 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 the 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 Complex Plane Viewer (CPV), a program written by myself for visualizing complex functions, developed within Lazarus IDE.