Explorables

Rainbows in the browser: follow sunlight through a raindrop, find the ray where light piles up, and see the primary bow, the reversed secondary and the dark band between them.

A four-bar linkage lab in the browser: drag the pivots and joints, turn the crank, and watch a point on the coupler trace loops, figure eights and nearly straight lines.

Cloth in the browser: hang a curtain, a banner or a flag from pins, grab, cut and tear it, and watch every thread coloured by how hard it is pulled.

The brachistochrone and the tautochrone in the browser: race beads from A to B along a ramp, an arc, the cycloid and a track you draw, then drop them into a cycloidal bowl where every start takes the same time.

The Mandelbrot set and its Julia sets side by side: pick c, follow the orbit of 0 and see which cycle it settles on.

Lenia in the browser: a continuous cellular automaton that grows gliding creatures. Place Orbium and its relatives, paint, and retune the rule live.

A wind tunnel in the browser: lattice Boltzmann flow past a cylinder, plate or wing, with vortex streets, streaklines and drawable walls.

The Doppler effect and the Mach cone in the browser: drag a listener, push the source past the speed of sound, and hear the boom and the backwards sound inside the cone.

A hard-disk gas in the browser: elastic disks collide in a box, their speeds settle into the Maxwell-Boltzmann curve and the wall pressure follows the hard-disk equation of state.

The Tonnetz in the browser: every triangle a triad, neo-Riemannian P/L/R moves, progressions traced as paths and voice leading you can hear.

Strange attractors in the browser: turn Lorenz, Rössler and five relatives in 3D and watch a speck of nearby starts spread over the attractor at the Lyapunov rate.

Wave function collapse in the browser: paint a small sample and watch a larger pattern woven from its local rules, one cell at a time.

Weighted Voronoi stippling in the browser: dots settle by Lloyd relaxation until their spacing draws the picture, then one continuous line visits them all.

A slime mould in the browser: particles that sense, turn, step and leave a trail grow transport networks between food.

Langton's ant and its many-coloured relatives in the browser: one turning rule per colour, long stretches of chaos, and the highways, squares and triangles that come out of it.

A sundial and sun-path lab in the browser: where the sun stands for any place, date and time, the shadow it casts, and why sundials and clocks disagree.

Schelling's segregation model in the browser: households happy as a minority still sort a mixed town into enclaves.

A Galton board in the browser: drop balls through rows of pegs and watch the bell curve build up, checked against the binomial and normal distributions.

Percolation in the browser: random grids, merging clusters and the spanning threshold.

Penrose tilings in the browser: grow kites and darts or rhombi by substitution and watch the golden ratio appear in the tile counts.

Paper marbling in the browser: float drops of ink, rake them with combs and swirls, and print the pattern.

Electric field lines and equipotentials in the browser: place and drag charges, watch the field reshape, and find the points where it vanishes.

A quantum wave packet in the browser: fire it at barriers, steps, wells and lattices, watch it split, and compare the measured transmission with the exact answer.

An L-system garden in the browser: write rewriting rules, grow plants and fractal curves with turtle graphics, and watch them unfold stroke by stroke.

Fireflies that learn to flash together: the Kuramoto model of coupled oscillators in the browser, checked live against the exact synchronization threshold.

An Abelian sandpile in the browser: pour towers, rain grains and watch avalanches, and find the sandpile group identity.

Grow snow crystals in the browser with Reiter's hexagonal cellular model.

A 2D optics bench in the browser: trace light through prisms, lenses and mirrors, with Fresnel splitting, total internal reflection and glass dispersion.

The 2D Ising model in the browser: cool a lattice of magnetic spins through its critical temperature and watch order appear.

A browser Chladni plate: sweep a tone and watch sand gather on the nodal lines of a vibrating square plate.

A browser harmonograph: damped pendulums steer a pen and trace slowly turning, decaying Lissajous figures you can tune, share and export.

An interactive traffic-jam lab: phantom jams on a ring road, a space-time diagram and a flow-density curve you map yourself.

An interactive double-pendulum chaos lab: release a fan of nearly identical pendulums and watch tiny differences grow into completely different motion.

An interactive reaction-diffusion pattern lab: paint seeds, tune feed and kill rates, and watch spots, stripes, corals and worms grow in the browser.

An interactive ripple tank: drop wave sources, draw walls and watch interference, diffraction, reflection and refraction in the browser.

An interactive flocking simulation: tune the rules that steer hundreds of boids and watch a flock emerge.

Draw a shape and watch a chain of rotating circles retrace it with the discrete Fourier transform.

An interactive pathfinding visualizer for grid search algorithms.

An interactive color-vision-deficiency simulator for images.

An interactive N-body gravity simulator for exploring orbital mechanics in the browser.