Chaos
15 interactive notebooks ready to launch.
// Unit 1: The Onset of Chaos (1D Dynamics)
Cobweb Plots and Fixed Points
Explore 1D dynamics by plotting cobweb diagrams and identifying fixed points.
The Bifurcation Diagram
Visualize how changing system parameters leads to bifurcations and period doubling.
The Butterfly Effect & Lyapunov Exponents
Quantify sensitivity to initial conditions using Lyapunov exponents.
// Unit 2: Symbolic Dynamics (The Math of the Shift)
Itineraries and The Tent Map
Represent chaotic trajectories with symbolic itineraries and study the tent map.
The Shift Space
Explore the shift space and its combinatorial structure in symbolic dynamics.
Topological Conjugacy
Learn when chaotic maps are equivalent through topological conjugacy.
// Unit 3: The Geometry of Chaos (Fractals)
Recursive Monsters
Generate fractal shapes through recursive algorithms and discover self-similarity.
Fractional Dimension & Box Counting
Estimate fractal dimension using the box-counting method.
The Chaos Game / IFS
Construct fractals with iterated function systems using randomized rules.
// Unit 4: Strange Attractors and Continuous Chaos
Stretching and Folding: Henon Map
Visualize discrete chaos through stretching and folding in the Henon map.
Slicing the Lorenz Attractor
Examine cross-sections of the Lorenz system and its famous attractor.
Basin Boundaries
Explore how basins of attraction form complex boundaries in chaotic systems.
// Unit 5: Cellular Automata and the Edge of Chaos
1D Automata & Wolfram Rule 30
Study one-dimensional cellular automata and the emergence of complexity.
Conway’s Game of Life
Simulate Conway’s cellular automaton to observe persistent patterns and growth.
Langton’s Lambda & Edge of Chaos
Measure the edge of chaos in cellular automata using Langton’s lambda parameter.