Table of Contents Last updated May 29, 2022 Save as PDF InfoPage 1: Quick tour Page ID103218 ( \newcommand{\kernel}{\mathrm{null}\,}\) "M-set anatomy" remake1: Quick tour1.1: Rotation Numbers and Internal angles of the Mandelbrot bulbs1.2: The primary Bulbs counting1.3: The Secondary Bulbs Symmetry1.4: The Third level Bulbs Symmetry2: Iterations of quadratic maps2.1: Iterations of real quadratic functions2.2: Bifurcation diagram for quadratic maps2.3: The Mandelbrot, Julia and Fatou sets2.4: Iterations of inverse quadratic maps3: The Julia set3.1: The Julia set symmetry3.2: Critical points and Fatou theorem3.3: The Fundamental Dichotomy for Julia sets4: Attractors, repellers...4.1: The fixed points and periodic orbits4.2: Local dynamics at a fixed point4.3: Spiral structures in the Julia sets4.4: Attracting Fixed point and Period 2 orbit4.5: Tangent bifurcations4.6: Period doubling bifurcations4.7: period tripling bifurcations4.8: Parabollic fixed points and Siegel disk5: Renormalization theory5.1: Windows of periodicity scaling, the "linear" approximation5.2: The Julia set5.3: The Mandelbrot set renormalization5.4: Polynomial-like maps5.5: Renormalization5.6: Rabbit's show5.7: Shaggy midgets6: Periodic and preperiodic points6.1: Periodic and preperiodic points in the M-set6.2: Misiurewicz points and the M-set self-similarity6.3: The M and J-sets similarity, Lei's theorem6.4: Embedded Julia midgets7: Shrubs ordering7.1: Shrubs ordering8: Illustrations8.1: The Julia set animation8.2: 600x600 Mandelbrot set with the Boundary Tracing8.3: Distance Estimator algorithms