Conway's Game of Life: from four local rules emerges an entire universe of gliders, oscillators, and self-replicating structures. Emergence is the central mystery — how does complexity arise from simplicity?
II. Chaos — Lorenz Attractor
The Lorenz attractor: a strange attractor with fractal structure and sensitive dependence on initial conditions. Two nearby trajectories diverge exponentially — the butterfly effect. The system is deterministic yet unpredictable.
III. Waves — 2D Wave Equation
Click anywhere to create ripples. Multiple sources create interference patterns — constructive where crests meet, destructive where crest meets trough. The wave equation ∂²u/∂t² = c²∇²u governs sound, light, and water waves.
IV. Networks — Barabási-Albert Scale-Free Growth
The Barabási-Albert model grows a network via preferential attachment: new nodes connect to existing nodes with probability proportional to their degree. This "rich get richer" rule produces a power-law degree distribution P(k) ∝ k⁻³, characteristic of the internet, social networks, and citations.
V. Quantum — Double-Slit Particle Buildup
Particles (electrons/photons) are sent one-at-a-time through a double slit. Each particle lands randomly, yet collectively they build up an interference pattern — unless a which-path detector is present, which collapses the wavefunction and destroys interference. Toggle the detector to see quantum complementarity.