Part 1. The Mandelbrot and Julia sets Anatomy
Contents

• Introduction
• Quick tour   Robert L. Devaney
  • Rotation numbers and internal angles of the M-bulbs
  • The primary M-bulbs counting
  • The secondary and The third level M-bulbs
  
  
• Iterations of quadratic maps
  • Iterations of real maps
  • Bifurcation diagram for quadratic maps
  • Iterations on the complex plane. The Mandelbrot, Julia and Fatou sets
• The Julia sets
  • The Julia sets symmetry     27 apr 06
  • Iterations of inverse maps
  • Critical points and Fatou theorem
  • The Fundamental Dichotomy for J-sets
• Attractors
  • The fixed points and periodic orbits
  • Local dynamics at a fixed point
  • Attracting fixed point and period-2 orbit
  • Tangent bifurcations
  • Period doubling and period trippling bifurcations
• Periodic and preperiodic points
  • Periodic and preperiodic points in the M-set
  • Misiurewicz points and the M-set self-similarity   Douglas C. Ravenel
  • The M and J-sets similarity. Lei's theorem   Douglas C. Ravenel
• "More" Mandelbrot sets
  • Polynomial maps
  • "Growth" in complex exponential dynamics
  • Quaternions & the Mandelbrot set
• Renormalization
  • "Linear" approximation. Midgets scaling
    Windows of periodicity scaling
    Renormalization on complex plane
    Multiple renormalization
    Inverse quadratic-like maps
  • Polynomial-like maps   Nuria Fagella
    Renormalization   Nuria Fagella
    Rabbits show
• Embedded midgets
  • Embedded Julia midgets. Nodes
  • Embedded Cantor-like midgets
• Symbolic dynamics
  • Windows of periodicity ordering
  • Symbolic dynamics magic
  • Windows of periodicity and Symbolic dynamics
• Crises
  • Boundary and interior crises
  • "Cosine" approximation
  • Scaling and ordering at the boundary and interior crisis points
  • Complex Crises
• Intermittency
  • Transition to chaos through intermittency
  • "Intermittent" periodic orbits
• Period doubling cascade
  • Universal scaling law
  • Period doubling bifurcations on complex plane
  • Reverse period doubling cascades
• Period n-tuplings cascade
  • Universal period n-tuplings cascade
  • The Primary (m/n) bulbs Zoo. More examples
  • Reverse period n-tuplings cascades
• Shrubs ordering   Miguel Romera

Part 2. Chaotic maps

• Illustrations (Controls, hints and tips)
  • Animated voyages
    • Julia Orbit trip (350x450)
    • "5 Stars" Julia trip (350x450)
    • Cantor, Caterpillar and Renormalization trips with DE
    • z^4 Julia Stars trip
  • 600x600 Mandelbrot set with the Boundary Tracing and
    Distance Estimator algorithms
    Big Bifurcation and Iteration diagrams
    Interactive Logistic map
  • 3D Mandelbrot and Julia sets

• References

All sources are free. Take the whole MSet.zip (21 Sept 03, 348kb). Collected by Evgeny Demidov