Interactive
Simulations
Small interactive explorables — each one picks the tool that fits the phenomenon. Start with a module below for a guided, build-from-first-principles path, or dive into any single sim.
Modules — multi-lesson deep dives
Course · 5 lessonsRandomness → the Bell Curve
Monte Carlo → walks → Galton → CLT → Bayes.
Explorable · deep diveWhy the Moon Has Phases
Built up step by step; drag the Moon.
Explorable · deep diveWhy a Bicycle Stays Up
From falling pendulum to self-steering trail.
Explorable · deep diveThe Road to Serfdom
Hayek's argument as an interactive book.
Physics & motion
Ripple Tank
Two-source wave interference; drag a source.
Canvas 2DCoulomb's Law
Drag charges and watch inverse-square forces.
SVGPendulum
Damped pendulum; drag the bob to set the angle.
Canvas 2DDouble Pendulum
Deterministic physics, chaotic motion.
ExplorableWhy a Bicycle Stays Up
Steering trail, not gyroscopes, self-balances it.
ExplorableCountersteering a Bike
Wrong-way steering creates the lean that starts a turn.
Canvas 2DOrbital Transfer
Hohmann transfer geometry and delta-v intuition.
Matter.jsPhysics Stack
Drop and drag rigid bodies.
Math
Computer science & AI
Sorting Race
Compare selection, insertion, and bubble sorting.
Canvas 2DGame of Life
Local rules create gliders, still lifes, and chaos.
Canvas 2DGradient Descent
Tune learning rate and momentum on a loss surface.
Canvas 2DBias-Variance
Polynomial degree trades underfit for overfit.
Canvas 2DK-Means Clustering
Assignments and centroids iterate toward clusters.
Canvas 2DNeural Boundary
A tiny network bends a decision field.
Canvas 2DMDP Gridworld
Value iteration diffuses rewards into a policy.
Canvas 2DPageRank Surfer
Random-surfer rank mass settles on a graph.
Canvas 2DA* Pathfinding
Heuristics steer a shortest-path search frontier.
Canvas 2DCSP Map Coloring
Backtracking searches for a conflict-free coloring.
Systems & control
SIR Epidemic
Transmission and recovery shape an epidemic curve.
Canvas 2DPID Control
Tune feedback gains to reach a moving target.
Canvas 2DKalman Filter
Estimate a hidden signal from noisy measurements.
Canvas 2DReaction-Diffusion
Local reactions and diffusion grow spots and stripes.
Canvas 2DPredator-Prey Cycles
Coupled populations loop through phase space.
Canvas 2DEnzyme Kinetics
Michaelis-Menten saturation from enzyme limits.
Canvas 2DGillespie Birth-Death
Stochastic event paths versus smooth expectation.
Canvas 2DForest Fire Automaton
Growth and lightning create clustered burn waves.
Canvas 2DRobot Arm IK
Drag a target and solve a two-link arm.
Canvas 2DM/M/1 Queue
Utilization near one makes waiting explode.
Statistics
Coupon Collector
The final missing coupon creates a long tail.
Canvas 2DBirthday Paradox
Shared birthdays appear sooner than intuition expects.
Canvas 2DBootstrap Resampling
Resample observed data to estimate uncertainty.
Canvas 2DGambler's Ruin
Random walks hit fortune or ruin boundaries.
Canvas 2DPercolation Threshold
Open sites suddenly form a spanning path.
Canvas 2DMarkov Chain Mixing
Transition steps converge toward stationarity.
Canvas 2DRandom Walk Diffusion
Independent steps spread into a widening cloud.
Canvas 2DMonte Carlo Pi
Random samples estimate area and uncertainty.
Canvas 2DBayes Test
Base rates explain why false positives dominate.
Canvas 2DGalton Board
Coin flips pile up into a bell curve.
Canvas 2DCentral Limit Theorem
Averages of any shape become a bell curve.
D3Interactive Bars
Data-driven chart with hover + regen.
Economics & finance
Supply & Demand
Shift curves; find the new equilibrium.
Canvas 2DOptions Payoffs
P/L diagrams for calls, puts, spreads.
Canvas 2D800 VDC Power Delivery
Higher voltage cuts current and busbar heat.
Canvas 2DSchelling Model
Local preferences produce global clustering.
Canvas 2DNetwork Cascade
Threshold adoption spreads or stalls on a graph.
Canvas 2DCongestion Pricing
Tolls reshape route choice and social cost.