Interactive experiments
I build interactive experiments when ideas get too interesting to leave as prose. These are things that got out of hand.
Reaction-diffusion
Two chemicals diffuse and react. Complex patterns emerge from simple local rules.
Strange attractors
The Lorenz system never repeats, never escapes. Deterministic chaos made visible.
Mandelbrot set
Infinite boundary complexity from a two-line rule. Zoom in forever.
Conway’s Life
Four rules. Three states. Enough to simulate anything a computer can compute.
Voronoi diagrams
Every point belongs to its nearest neighbor. Cells of belonging.
Bifurcation diagram
A single parameter drives order into chaos — and back out again.
Gradient descent
How machine learning learns: a ball rolling downhill on a landscape you can shape.
Penrose tiling
Tiles that cover the plane without ever repeating. Almost periodic.
The missing fundamental
Your brain infers a pitch that isn’t in the signal. Inference, not illusion.
Network dynamics
How opinions spread through networks. Topology shapes consensus — or prevents it.
Slime mold
A brainless organism builds efficient transport networks. Thousands of agents, no plan, emergent optimization.
Bioluminescence
Disturb the water. Thousands of dinoflagellates flash in chain reactions — the ocean’s burglar alarm.
Sandpile
Drop grains of sand. Watch them topple. Fractals emerge from the simplest possible rule — self-organized criticality.
Elementary cellular automata
256 one-dimensional rules. Some produce nothing. Some produce chaos. One is Turing complete. Time flows downward.
Percolation
Adjust a single probability. At the critical threshold, isolated clusters suddenly connect into a spanning network.
Diffusion-limited aggregation
Random walkers stick on contact. Fractal dendrites emerge — snowflakes, lightning, and mineral veins from pure randomness.
L-systems
Rewriting rules become fractal geometry. Axiom, grammar, turtle — and plants that never existed grow from pure syntax.
Double pendulum
Two arms, deterministic equations, and wildly unpredictable motion. The simplest system where certainty dissolves into chaos.
Fourier transform
Any signal is just a sum of sine waves. Draw a waveform, watch it decompose, build one from harmonics, and see epicycles trace the shape.
Wave interference
Drop point sources into a ripple tank. Watch waves superpose, interfere, and diffract. The physics of superposition, visible.
Evolutionary game theory
Cooperators and defectors compete on a grid. Spatial structure enables cooperation that pure logic forbids. Watch strategies evolve.
Lotka-Volterra
Two species, four parameters. The predator-prey dance that never settles — orbits that close but never repeat exactly.
Ciphers
Type a message, encrypt it, then break it with frequency analysis — the technique Al-Kindi invented in 850 CE Baghdad.
Schelling segregation
Mild individual preferences produce dramatic collective segregation. The gap between personal tolerance and social outcomes, visualized.
Galton board
Balls bounce randomly through pegs and pile into a bell curve. The central limit theorem — order from pure randomness.
Chaos game
Pick a random vertex. Jump halfway. Repeat. Somehow, a fractal appears — order from pure randomness and a simple rule.
Ising model
A lattice of spins, each choosing up or down. Below a critical temperature, order emerges spontaneously — a phase transition from thermal chaos into collective magnetism.
Random walk
Walkers take random steps and trace unpredictable paths — yet from pure chaos, the bell curve emerges. Diffusion, Brownian motion, and the square-root law made visible.
Dead reckoning
Navigate by integrating noisy measurements from a known start. Watch error accumulate, experiment with corrections, and see why every integrating system drifts without ground truth.
Boids
Three simple rules — separation, alignment, cohesion — and complex flocking emerges with no leader and no global plan. Craig Reynolds’ 1987 algorithm, the science of self-organization made visible.
Ant pheromone trails
No leader, no map, no plan. Ants leave chemical traces that recruit others, and efficient foraging trails emerge from pure local interaction — stigmergy, the coordination mechanism that scales from termites to Wikipedia.
N-body gravity
Every mass pulls every other mass. The two-body problem is solved; the three-body problem is chaos. Add bodies, launch them with velocity, and watch orbits form, destabilize, and eject.
Voting systems
Same voters, same preferences, different winners. Five voting methods applied to the same ballots — Arrow’s impossibility theorem made interactive.