Chaotic Fractals

Visual chaos of strange attractors

• Deterministic chaos
  • Laplace’s daemon, Pierre-Simon Laplace
  • Dynamical systems, nonlinear system, ergodic theory, chaos theory
  • Stability, bifurcation, edge of chaos, butterfly effect, Feigenbaum constants
  • Population dynamics, logistic function, logistic map, Robert May
  • Attractor, strange attractors
• Discrete dynamical systems
  • Gaussian map, Hénon map, standard map, exponential map, coupled map lattice, Lyapunov fractal, Arnold’s cat map, Ikeda map
  • Michel Hénon, Aleksandr Lyapunov, Vladimir Arnold, Kensuke Ikeda
• Continuous dynamical systems
  • Ordinary differential equations, Euler method, Poincaré–Bendixson theorem
  • Three body problem, Leonhard Euler, Henri Poincaré
  • Lorenz attractor, Rössler attractor, multiscroll attractors
  • Edward Lorenz, Otto Rösler
  • Self-organization, flocking

Discussion

• Chaos Theory (World of Mathematics)
• Fractals, Chaos, Self-Similarity (Paul Bourke)
• The Chaos Hypertextbook (Glenn Elert)
• Chaos: A Mathematical Adventure (Jos Leys, Étienne Ghys & Aurélien Alvarez)
• Math:Rules – Strange Attractors (Chaotic Atmospheres)
• Chaoscope Tutorial

Assignment

Strange attractors

a-Traktor – Atraktor – Attract Explorer – Attractors – Chaoscope – glChAoS.P – Interactive Lorenz – Visions of Chaos

 

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