Simulations & math toys

Epidemics, traffic jams, cellular automata, fractals and drawing with circles — classic models you can poke at, running live in your browser.

Simulations

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Gerrymandering Sandbox

Draw the districts yourself and watch the same voters produce opposite election results.

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Pareto Frontier Evolution

Watch a genetic algorithm breed bridge designs and trace out the weight-vs-stiffness Pareto frontier, generation by generation.

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SIR Epidemic Simulator

Watch an epidemic spread and burn out with the classic susceptible–infected–recovered model.

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Sailing & Tacking Simulator

Sail a boat against the wind — trim to the polar diagram, ride the shifts and race the optimal route.

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Schelling’s Segregation Model

Give agents a mild preference for similar neighbours and watch a mixed city sort itself into stark blocks.

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Traffic Jam Simulator

See phantom traffic jams appear from nothing on a ring road with the Nagel–Schreckenberg model.

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Tsunami Simulator

Set off an undersea earthquake anywhere and watch the tsunami cross real ocean floors — with arrival times at tide gauges around the world.

Airplane Boarding Simulator

Race back-to-front against WILMA and Steffen on the same plane — heat-map the aisle jams, toggle bag stow, and try a widebody.

Auction Strategy Lab

Bid in first-price, Vickrey, English and Dutch auctions — and meet the winner’s curse in person.

Braess’s Paradox

Open a free shortcut and watch every commute get longer — the road-network paradox, live.

Bullwhip Effect (Beer Game)

A tiny bump in customer demand becomes a factory earthquake — the supply-chain classic, fully automated.

City Traffic Grid

Route cars through a grid of light-controlled intersections and watch gridlock form and clear.

Crowd Evacuation Simulator

Empty a crowded room through one door — and test the paradox that an obstacle can speed the escape.

Economy Sandbox

Run a miniature economy of households and firms — set taxes, print money and watch GDP, inflation and inequality respond.

Forest Fire Model

Grow a forest, strike it with lightning and watch fires balance growth into self-organised criticality.

Iterated Prisoner’s Dilemma Tournament

Pit Tit for Tat against defectors, grudgers and gamblers — then let evolution decide who inherits the population.

Opinion Spread

Watch opinions ripple through a social network and settle into consensus, polarisation or stubborn echo chambers.

Order Book & Market Maker

Watch a live limit order book breathe — and run a market maker through order flow, slippage and a flash crash.

Plate Tectonics Toy

Drifting plates collide into mountain ranges, tear open rift oceans and dive into trenches — on a planet you control.

Predator–Prey Simulator

Explore boom-and-bust population cycles with the Lotka–Volterra equations.

Queue Simulator

One line or one per till? Watch waiting-time theory come alive as customers queue, jockey and fume.

River Erosion

Rain carves branching valleys into a hillshaded landscape — and a lowland river meanders itself into oxbow lakes.

Small-World Network Lab

Rewire a ring lattice into a small world and watch six degrees of separation appear.

Sugarscape

Let simple agents forage a landscape of sugar and watch a stark wealth distribution emerge on its own.

Tragedy of the Commons

Fish a shared stock with greedy boats and watch it collapse — then save it with quotas or taxes.

Wealth Inequality (Yard-Sale Model)

Fair coin flips, equal starts — and one agent still ends up with everything. Then tax it and watch it stabilise.

Zipper Merge Simulator

Merge early or ride the closing lane to the end? Simulate the lane-drop and let throughput settle the argument.

Physics

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Buoyancy Tank

Drop blocks of different density into water and watch Archimedes decide what floats, sinks or hovers.

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Double Pendulum

Swing a chaotic double pendulum and split it into a rainbow swarm to watch nearby starts diverge.

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Falling-Sand Playground

Paint sand, water, oil, fire and more and watch them pour, settle, burn and react pixel by pixel.

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Fluid Flow Simulator

Stir glowing dye through a real-time GPU fluid simulation.

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Galaxy Collision Simulator

Smash two spiral galaxies together and watch tidal tails and bridges form.

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Hear the Shape of a Drum

Draw any drum and hear its true vibration modes — then meet two different drums that sound exactly the same.

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Orbit Sandbox

Fling planets around a star and watch Newtonian gravity draw ellipses, slingshots and chaotic dances.

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Special Relativity Visualizer

Accelerate toward light speed and watch length contraction, time dilation and the Doppler shift warp a star field.

Bicycle Stability

Shove a riderless bike and watch it catch itself — the benchmark model behind self-stability and countersteering.

Black Hole Lensing

Watch an accretion disk warp around a black hole through real gravitational lensing.

Brownian Motion

Watch a big particle jitter as thousands of invisible molecules bombard it, and see its path wander.

Chladni Plate Patterns

Vibrate a square plate and watch sand grains gather into Chladni’s nodal-line figures.

Cloth Simulator

Drag, tear and cut a hanging cloth simulated with Verlet physics.

Coriolis Effect

One ball, two cameras: a straight roll turns into a curve when the camera spins with the disk.

Domino Run

Line up dominoes, tip the first and watch the toppling wave race down the chain with rigid-body physics.

Gyroscope Precession

Why a spinning wheel on a string circles sideways instead of falling — watch precession and nutation live in 3D.

Lightning Simulator

Grow branching electric discharges that strike the ground and flash.

Magnetic Field Lines

Drag bar magnets around and watch animated iron filings sketch the field lines between them.

Magnus Effect

Curveballs, banana free kicks and golf drives: how spin bends a ball’s flight through the air.

Ray Optics Bench

Shine rays of light through lenses, mirrors and prisms and watch them bend, focus and split into a rainbow.

Soft-Body Jelly

Drop, drag and squash wobbly spring-mass blobs that jiggle and bounce like jelly.

Standing Waves on a String

Drive a string at any frequency and watch it burst into resonance at the harmonics.

Tides Simulator

Why the ocean bulges on both sides of the Earth — spring tides, neap tides and the 12h25m rhythm.

Wave Interference

Drop oscillating sources into a virtual ripple tank and watch interference fringes and the double slit emerge.

Harmonograph

Let damped pendulums draw glowing Lissajous figures, the Victorian way.

Chemistry

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Diffusion & Osmosis

Split a tank with a semipermeable wall and watch particles diffuse and water flow to equalise concentration.

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Ideal Gas & Maxwell–Boltzmann

Bounce hard-disc molecules in a box and watch their speeds settle into the Maxwell–Boltzmann distribution.

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Reaction–Diffusion Patterns

Grow coral, spots and zebra stripes from two virtual chemicals with the Gray–Scott model.

Belousov–Zhabotinsky Reaction

Watch an oscillating chemical medium organize itself into rotating spiral waves.

Crystal Growth Simulator

Grow branching fractal crystals one wandering particle at a time with diffusion-limited aggregation.

Flame Simulator

Paint fire and shape a living flame with fuel, cooling, wind and turbulence.

Ising Model Ferromagnet

Flip a grid of spins at any temperature and watch magnetic domains freeze in or melt at the critical point.

Molecular Dynamics: Phases of Matter

Cool a two-dimensional Lennard-Jones fluid from hot gas through droplets to a hexagonal crystal.

Percolation

Randomly fill a grid and find the tipping point where a path first spans it from side to side.

Biology

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Boids Flocking Simulator

Watch lifelike flocking emerge from three local rules with Reynolds’ boids model.

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Lenia Continuous Life

Grow smooth self-organising lifeforms like the gliding Orbium in a continuous cellular automaton.

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Particle Life

A few coloured species and one table of likes and dislikes — and cells, chains and chasing creatures emerge by themselves.

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Slime Mould Networks

Watch millions of Physarum agents self-organise into living transport networks.

Ant Colony Pheromone Trails

Watch ants self-organise foraging highways with evaporating pheromone trails.

Evolving Creatures

See natural selection reshape a population of foraging creatures generation by generation.

Firefly Synchronization

See a meadow of fireflies fall into spontaneous unison as pulse-coupled oscillators.

Genetic Drift Simulator

See how chance alone fixes or loses gene variants in small populations with the Wright–Fisher model.

Immune System vs Infection

Release a pathogen in a tissue and watch immune cells hunt it down before it overwhelms the body.

L-System Plants

Grow fractal ferns and trees from tiny grammars with Lindenmayer systems.

Mycelium Growth

Grow organic root, vein and fungal networks with the space-colonization algorithm.

Neuron Action Potential

Fire a nerve impulse and explore thresholds and refractory periods with the FitzHugh–Nagumo model.

Spiking Neuron Network

Wire up a grid of spiking neurons and watch waves of activity ripple, echo and synchronise.

Math Toys

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3D Geometry Board

Points, lines, planes, spheres and polyhedra on an orbiting camera — slice solids with planes, unfold nets, drop the Dandelin spheres into a cone and drag everything.

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Bézier Curve Playground

Drag control points and watch De Casteljau’s algorithm construct a Bézier curve step by step.

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Central Limit Theorem Demo

Sample from any lopsided distribution and watch the averages pile up into a bell curve.

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Conway’s Game of Life

Paint cells and watch Conway’s cellular automaton breed gliders, guns and oscillators.

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Dynamic Geometry Board

Construct with points, lines, circles and transformations, then drag anything — the construction stays true, and a checker tells you which relations are theorems.

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Fantasy Map Generator

Roll a seed and get a continent: coastlines, mountains, rivers, biomes and named towns, ready for your campaign.

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Fifteen Puzzle

Slide the tiles back into order — and learn the parity argument that makes half of all positions impossible.

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Fourier Series Builder

Stack spinning circles to build square and sawtooth waves, and meet the Gibbs overshoot at the corners.

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Galton Board

Drop thousands of balls through a peg board and watch a bell curve build itself from pure chance.

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Guess the Correlation

A scatterplot appears — guess its correlation r, then see how close you got and build a streak.

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Interactive Unit Circle

Drag the angle around the circle and watch sine, cosine and tangent draw themselves.

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Julia Set Explorer

Slide the complex parameter c and morph the Julia set through dust, dendrites and swirling islands.

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Knight’s Tour

Guide a knight to visit every square exactly once — or let Warnsdorff’s rule find the tour instantly.

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Linear Transformation Playground

Drag the matrix, watch the grid shear, rotate and flip — see what a 2×2 matrix really does.

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Lorenz Attractor

Trace the butterfly-shaped strange attractor that gave chaos theory its name, in rotating 3D.

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Monte Carlo Playground

Throw random samples and watch the truth emerge — estimate π, integrals, retirement odds and even perfect game moves from pure noise.

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Monty Hall Simulator

Play the three-door game and watch the win rate settle on 2/3 for switching and 1/3 for staying.

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N-Queens Visualizer

Watch backtracking place queens, hit dead ends, retreat and finally crack the N-queens puzzle.

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Nim & Grundy Numbers

Play Nim against perfect XOR strategy and learn why the binary digital sum decides every game.

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Sieve of Eratosthenes

Cross out the multiples one prime at a time and watch the primes reveal themselves.

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Simpson’s Paradox Visualizer

Watch a trend reverse when groups are merged — each group slopes up, the pooled data slopes down.

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Three-Body Choreographies

Launch three equal stars into the figure-eight orbit and other periodic dances, then perturb them into chaos.

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Tower of Hanoi

Solve the classic disc puzzle yourself or watch the optimal 2ⁿ − 1 recursion unfold.

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Wallpaper Group Designer

Draw a motif, pick one of the 17 plane symmetry groups and the whole plane fills with its orbit — mirrors, glides and rotation centres marked, seamless tile and SVG export.

3D Surface Plotter

Spin saddles, ripples and peaks in 3D and see functions of two variables come alive.

A/B Test Peeking Simulator

Check your A/B test daily and stop at p < 0.05 — and your false-positive rate isn’t 5%, it’s 30%.

Abelian Sandpile

Drop millions of sand grains on one spot and watch a perfectly symmetric fractal mandala grow.

Base Rate Visualizer

A 99%-accurate test says you’re sick — the odds you actually are can still be tiny. See why with 1000 dots.

Berkson’s Paradox

Two traits with zero correlation turn negatively correlated the moment you select on their sum.

Bootstrap Resampling Visualizer

Resample one dataset with replacement thousands of times to build a confidence interval from nothing but itself.

Brachistochrone Race

Race beads down a straight ramp, a circular arc and a cycloid — the sagging curve wins every time.

Buffon’s Needle

Drop needles on a lined floor and estimate π from how often they cross a line.

Chaos Game

Jump halfway to a random corner over and over and watch the Sierpiński triangle appear from pure randomness.

Collatz Orbits

Follow the 3n+1 hailstone sequences and grow them into a branching coral of every number’s path.

Compression Playground

Watch RLE, LZ77 and Huffman coding squeeze text token by token, with every byte of input tied to its share of the output.

Einstein Monotile

The 2023 “hat” and “spectre”: one single tile that covers the plane without ever repeating.

Elementary Cellular Automata

Generate Wolfram’s one-dimensional rule 30, 90 and 110 patterns from a single cell.

Euclidean Algorithm Visualizer

Tile a rectangle with the biggest squares that fit and read off the greatest common divisor.

Euler vs Runge–Kutta

Race Euler’s method against RK4 on the same equation and watch the cheap method drift off course.

Flow-Field Particles

Set thousands of particles adrift on a field of Perlin noise and watch them weave silky ribbons.

Four Color Map

Color a random map with four colors — the theorem says you always can, the puzzle is finding how.

Fourier Epicycles

Draw a shape and watch a chain of rotating circles redraw it from its Fourier series.

Heat Equation Simulator

Watch a hot spot melt into a smooth bell and spread through a rod as the heat equation does its work.

Hilbert Curve Explorer

Watch one continuous line snake through every cell of a square — a curve with dimension 2.

Kaleidoscope

Draw with the pointer and see your strokes mirrored into live n-fold symmetric mandalas.

Langton’s Ant

Two rules, total chaos, then a highway: watch the famous ant build order out of mess after 10,000 steps.

Law of Large Numbers

Watch the running average of dice or coins settle onto the expected value as trials pile up.

Logistic Map Bifurcation

Sweep one parameter of the logistic map and watch order split, split again and dissolve into chaos.

Magic Square Builder

Generate magic squares of any size and watch every row, column and diagonal sum to the same number.

Magnetic Pendulum Fractal

Swing a pendulum over three magnets and colour the plane by which one it lands on — a fractal appears.

Mandelbrot Explorer

Pan and zoom into the Mandelbrot set with smooth colouring and endless fractal detail.

Metaballs

Blend glowing blobs with a smooth field so they merge and split like a lava lamp.

Modular Times Table

Join each number to its multiple on a circle and watch cardioids and nested loops bloom.

Newton Fractal

Colour every starting point by the root Newton’s method finds and watch fractal basins appear.

Nontransitive Dice

Meet Efron’s dice, where A beats B beats C beats A — and let the loser pick first.

Pascal’s Triangle mod n

Colour Pascal’s triangle by remainder and watch Sierpinski triangles appear.

Penrose Tiling Generator

Grow the famous aperiodic tiling from two rhombus shapes that can cover the plane but never repeat.

Phyllotaxis

Place seeds by the golden angle and watch a sunflower head of interlocking Fibonacci spirals grow.

Platonic Solids Explorer

Spin all five perfect solids and check Euler’s formula V − E + F = 2 on each.

Random Walk Explorer

Send drunkards wandering across the plane and watch diffusion, Lévy flights and self-avoiding paths.

Regression to the Mean

Why rookies slump, funds fade and punishment “works” — the top performers were lucky, and luck doesn’t repeat.

Root-Finding Visualizer

Watch bisection crawl, Newton leap and the secant method split the difference, iteration by iteration.

Secretary Problem

Test the 37% rule for optimal stopping: look, then leap at the first candidate beating everyone so far.

Slope Field Explorer

See a differential equation as a field of tiny slopes, then click to release solution curves through it.

Spirograph

Roll a gear inside or outside another and trace the looping hypotrochoid and epitrochoid curves.

St. Petersburg Paradox

Play the coin game whose fair price is infinite yet almost always pays a few coins.

Starfield Warp

Fly through an endless 3D star tunnel and push the throttle toward a hypnotic warp-speed streak.

Tesseract Projection

Rotate a 4D hypercube and watch its shadow dance in your 3D world.

Truchet Tiles

Fill a grid with randomly rotated tiles and watch endless mazes, weaves and flowing curves appear.

Ulam Prime Spiral

Spiral the whole numbers outward, mark the primes and watch mysterious diagonal streaks appear.

Vector Field Visualizer

Release thousands of particles into a vector field and see divergence and curl with your own eyes.

Voronoi & Lloyd Relaxation

Scatter points, colour the region nearest each one, then relax them into an even honeycomb.

Wave Function Collapse

Watch a tile solver ripple across a grid, collapsing possibilities into one seamless pattern.

Zipf & Heaps' Law Explorer

Paste any book and watch its words line up on the log-log slope Zipf predicted — then see its vocabulary grow by Heaps’ law.

p-Hacking Simulator

Run dozens of pointless tests on pure noise and watch a "significant" result appear by chance.

Box-Counting Dimension Lab

Lay finer and finer grids over a fractal and measure its dimension from the slope of a log–log line.

Ford Circles & Farey Fractions

See every fraction as a circle kissing the number line, built from mediants of the Stern–Brocot tree.

Goldbach Comet

Plot how many ways each even number splits into two primes and watch a comet take shape.

Hyperbolic Tiling Explorer

Tile the Poincaré disk with polygons that would never fit in flat space, Escher-style.

Hénon Map Attractor

Iterate two little equations and watch a boomerang-shaped strange attractor with fractal layers appear.

Map Projection Distortion

Compare map projections with Tissot circles and see where each one lies to you.

Quaternion Rotation Visualizer

Rotate a 3D cube with an axis and angle and read off the quaternion that does it.

Computer Science

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CPU Scheduling Simulator

Run FCFS, SJF, SRTF, Round Robin, Priority and MLFQ on your processes and get the Gantt chart and waiting times.

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Dynamic Programming Visualizer

Watch edit distance and knapsack fill their tables cell by cell — dynamic programming with the lid off.

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Graph Algorithm Playground

Build a graph by clicking, then watch BFS, DFS, Dijkstra and Prim explore it live.

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Huffman Coding Visualizer

Type any text and watch the optimal prefix code assemble itself as a tree, rare letters sinking deepest.

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Pathfinding Visualizer

Draw walls and watch A*, Dijkstra, greedy and breadth-first search hunt for the shortest path.

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Sorting Algorithm Visualizer

Watch bubble, insertion, merge, quick and heap sort race through the same shuffled bars.

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Turing Machine Simulator

Watch a Turing machine read, write and shuffle along its tape — computation stripped to its atoms.

Hamming Code Playground

Flip any bit of a Hamming-encoded message and watch the parity checks point straight at the culprit.

Regex to Automaton

See a regular expression become a finite automaton and watch it accept or reject strings character by character.

Engineering & Technology

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Airfoil Designer & Analyzer

Shape a NACA airfoil, see its pressure distribution and plot lift and drag polars, XFOIL-style, in the browser.

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Bottle Rocket Simulator

Fill a soda-bottle water rocket, pump it up and launch it: find the water level, pressure and fins that fly highest.

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Bridge Builder & Truss Simulator

Design a truss bridge, send a truck across and watch every member strain, buckle or snap under load.

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Circuit Simulator

Build analog circuits on a grid and watch current flow live — batteries, resistors, capacitors, LEDs and more.

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Earthquake Shake Table Simulator

Shake a multi-story building with an earthquake and watch it sway, crack or survive, with base isolation and dampers.

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Gear Generator

Design involute spur gears, racks and planetary sets, watch them mesh and export SVG or DXF for laser cutting.

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Nuclear Reactor Simulator

Run a pressurized-water reactor: pull control rods, manage xenon and temperature — or SCRAM before it overheats.

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Orbital Mission Planner

Plan an interplanetary transfer: pick two planets, scan launch windows on a porkchop plot and fly the mission.

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PID Controller Simulator

Tune Kp, Ki and Kd on a car, a water tank, an oven or a drone and watch the step response settle or oscillate.

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Power Grid Simulator

Run an electric grid through a full day — dispatch plants, hold 50 Hz and survive cascading failures.

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Rocket Designer & Staging Lab

Build a multi-stage rocket, launch it, and see if your design reaches orbit.

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Roller Coaster Designer

Build a roller coaster hill by hill, add loops, and ride it: see the g-forces, the speed and where the energy goes.

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Room Acoustics Simulator

Draw a floor plan, clap, and watch the sound bounce — then hear any sound as it would ring in that room.

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Topology Optimizer

Say where a part is held and pushed, and watch the stiffest possible structure grow — then export it as SVG or STL.

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Will It Fit? Furniture Moving Planner

Enter your sofa and your doorway, hallway, stairs or elevator: a 3D motion planner finds the tilts and turns that get it through, or proves that nothing can.

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Wind Tunnel (CFD Sandbox)

Draw any shape into a virtual wind tunnel and measure its drag and lift in a live fluid simulation.

Elevator Dispatch Simulator

Watch elevator algorithms fight morning rush hour — and see why the smart building sends you to car C.

Linkage & Mechanism Simulator

Build four-bar, crank-slider and Strandbeest linkages, turn the crank and trace the curves they draw.

About these tools

Interactive simulations and mathematical toys: epidemic models, traffic flow, cellular automata like Conway’s Game of Life, fractals, random walks and other animated systems. Adjust the parameters and watch the behavior change in real time — a hands-on way to build intuition for complex dynamics.

Simulations & math toys

Most popular

3D Geometry Board

Airfoil Designer & Analyzer

Boids Flocking Simulator

Bottle Rocket Simulator

Bridge Builder & Truss Simulator

Buoyancy Tank

Bézier Curve Playground

CPU Scheduling Simulator

Central Limit Theorem Demo

Circuit Simulator

Conway’s Game of Life

Diffusion & Osmosis

Double Pendulum

Dynamic Geometry Board

Dynamic Programming Visualizer

Earthquake Shake Table Simulator

Falling-Sand Playground

Fantasy Map Generator

Fifteen Puzzle

Fluid Flow Simulator

Fourier Series Builder

Galaxy Collision Simulator

Galton Board

Gear Generator

Gerrymandering Sandbox

Graph Algorithm Playground

Guess the Correlation

Hear the Shape of a Drum

Huffman Coding Visualizer

Ideal Gas & Maxwell–Boltzmann

Interactive Unit Circle

Julia Set Explorer

Knight’s Tour

Lenia Continuous Life

Linear Transformation Playground

Lorenz Attractor

Monte Carlo Playground

Monty Hall Simulator

N-Queens Visualizer

Nim & Grundy Numbers

Nuclear Reactor Simulator

Orbit Sandbox

Orbital Mission Planner

PID Controller Simulator

Pareto Frontier Evolution

Particle Life

Pathfinding Visualizer

Power Grid Simulator

Reaction–Diffusion Patterns

Rocket Designer & Staging Lab

Roller Coaster Designer

Room Acoustics Simulator

SIR Epidemic Simulator

Sailing & Tacking Simulator

Schelling’s Segregation Model

Sieve of Eratosthenes

Simpson’s Paradox Visualizer

Slime Mould Networks

Sorting Algorithm Visualizer

Special Relativity Visualizer

Three-Body Choreographies

Topology Optimizer

Tower of Hanoi

Traffic Jam Simulator

Tsunami Simulator

Turing Machine Simulator

Wallpaper Group Designer

Will It Fit? Furniture Moving Planner

Wind Tunnel (CFD Sandbox)

Simulations

Gerrymandering Sandbox

Pareto Frontier Evolution

SIR Epidemic Simulator

Sailing & Tacking Simulator

Schelling’s Segregation Model

Traffic Jam Simulator

Tsunami Simulator

Airplane Boarding Simulator