Math Art in 3D: Fractals, Strange Attractors & Chaos
Some of the most beautiful shapes in nature come from a single line of maths. Here you can steer chaotic systems, fly through fractals, draw with gears and pendulums, and see simple rules grow intricate patterns, with each formula explained in plain language.
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Lorenz AttractorDrop probe clouds into the butterfly of chaos and watch them part. -
The Butterfly EffectStart two twins a millionth apart and see how soon they part ways. -
Mandelbulb Fractal FlightDive into a bronze Mandelbulb, a 3D cousin of the Mandelbrot set. -
Sunflower Golden AngleChange the angle between seeds and see why sunflowers use 137.5°. -
L-System BonsaiPrune, water and bend a bonsai grown from a few rewriting rules. -
Turing PatternsPaint on a fish’s skin and watch spots and stripes form by themselves. -
Rössler AttractorPull one lever: one loop doubles, doubles again, then turns to chaos. -
Aizawa AttractorDrop probes on a glowing shell and watch them shoot up its core. -
Thomas AttractorDrop probes into a looping knot and set them loose in a labyrinth. -
Halvorsen AttractorDrop probes into a three-lobed knot made by one rule used three ways. -
Chua’s Circuit Double ScrollTune a chaotic circuit with a knob and drop probes on its scope trace. -
Chen AttractorDrop probes into a fiery cousin of Lorenz’s butterfly, twice as wild. -
Harmonograph Drawing MachinePush a swinging table and let a pen draw spirals, stars and roses. -
Menger SpongeCarve a cube into a sponge with endless surface and almost no volume. -
Barnsley FernCurl, plant and follow a fern drawn by random dots and four rules. -
Möbius StripSet an ant on a paper Möbius strip, then cut the loop down the middle. -
Klein BottleWalk an ant through a glass bottle with no inside, then split it in two. -
Game of Life in 3DPoke and seed glowing cells in a glass tank and see 3D Life evolve. -
The Five Platonic SolidsFold plywood nets into the five Platonic solids and check Euler’s rule. -
Galton BoardDrop steel balls through brass pins and tilt the board to skew the odds. -
Spiral Gear ArtRoll a toothed wheel round a ring with a pen and draw roses and stars. -
Puzzle CubeTurn the faces of a real 3×3 cube, scramble it and solve it again. -
Soap Film SurfacesDip wire frames in soap and stretch films into minimal surfaces.