Between contests, a few mathematical toys. Each one runs entirely in your browser: turn the knobs, see what happens, and read where the idea came from.
From Al Zimmermann's 2010 contest
A computer searches for magic squares that hold the most rainwater, live in your browser. Load any record square, turn it in 3D, and try to beat it.
Simulated Annealing · Optimization · Magic Squares Open Retaining Water →
A nod to the sculpture prizes
Build a gyroid or one of its cousins, trim it to a sphere, cube or ring, check that it will print, and download the STL to print your own.
Geometry · 3D Printing Open Lattice Foundry →
Julia, 1918 · Mandelbrot, 1980
Dive into the Mandelbrot set, see the Julia set behind any point, and try the Burning Ship, the Tricorn, higher powers and Newton's method.
Fractals · Chaos Theory · Complex Numbers Open Fractal Explorer →
Sierpiński, 1915 · Barnsley, 1988
Click a few points, then jump toward them at random, a million times. Out of the noise comes Sierpiński's triangle, or a snowflake, or a carpet.
Fractals · Chaos Theory · Randomness Open The Chaos Game →
Chaos theory
One pendulum swings like a clock. Hang another from it and it never repeats. Start ten of them a ten-thousandth of a degree apart and watch them part company.
Chaos Theory · Physics · Simulation Open Pendulums →
Joseph Fourier, 1807
Draw any shape and watch a chain of spinning circles trace it. Start with one circle and add more: a blob sharpens into your drawing.
Fourier Series · Waves · Complex Numbers Open Can circles draw anything? →
Genetic algorithms, 1975
A genetic algorithm builds bikes from random parts and races them over hills that never stop growing. The furthest riders breed. Watch random junk turn into climbers.
Genetic Algorithm · Evolution · Optimization · Simulation Open Evolving Bikes →
John Conway, 1970
A grid of cells and three simple rules, with no player at all. Draw a few cells, press play, and watch gliders crawl, oscillators blink and a gun fire forever.
Emergence · Cellular Automata · Computation Open The Game of Life →
Craig Reynolds, 1986
Hundreds of birds, each following three simple rules about its neighbours. Nobody leads, and a flock appears anyway. Play the hawk and watch it split.
Emergence · Swarm Intelligence · Simulation Open Boids →
A few lines of BASIC, 2020 onwards
The "Bubble Universe": a few lines of sine and cosine that draw a swirling orb, as ZX Spectrum BASIC (at real 1982 speed, if you're patient) or in full colour.
Generative Art · Retro Computing Open Bubbleverse →
Steganography, since 1499
Hide a secret message in random colours or your own photo: plain, scrambled, or encrypted with a password and salt, in order or scattered. Save it, send it, read it back. (This card is hiding one too.)
Steganography · Cryptography · Binary Open Pixel Smuggler →No toys match. Pick a topic above.
