A small interactive museum · six exhibits
Small windows
into the infinite.
A cabinet of patterns, primes, chaos, and the strange places where simple rules go to bloom. Everything here is computed in your browser from arithmetic—no images, no libraries.
- 06
- living exhibits
- ∞
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Fourier's
drawing machine
Take a handful of circles, pin each one to the edge of the last, and let them spin. The tip of the final arm can trace any closed curve you like—a heart, a star, an infinity sign. This is the Fourier series, the same trick behind JPEGs, MP3s, and noise-cancelling headphones.
What to notice With a few terms you get a wobbly sketch. Add terms and the curve sharpens: the tiny circles are the high frequencies doing the fine detail.
The primes
decide to dance
Write the numbers 1, 2, 3… in a square spiral. Then light up the primes. Nobody asked them to line up, yet they fall into suspicious diagonals—polynomials in disguise. Stanisław Ulam reportedly doodled this during a boring lecture in 1963.
What to notice The bright diagonals correspond to quadratic expressions such as 4n² − 2n + 41. Dark gaps and bright streaks are number theory becoming visible.
calculating…
The edge
of chaos
Feed a number into x ← r x (1 − x), over and over. Change r and the long-term behaviour splits, doubles, splits again—then collapses into chaos. One line of arithmetic contains universality: the same bifurcation pattern appears in populations, lasers, and dripping faucets.
What to notice At r ≈ 3.5699 the period-doubling cascade ends. Inside the chaos are pale vertical windows where order suddenly returns.
r = 2.4 → 4.0
A coastline
that never ends
Iterate z ← z² + c for every point c in the plane, and colour each point by how long it takes to escape. The boundary between escape and imprisonment is infinitely intricate: zoom in forever and new copies of the whole set appear.
What to notice The black region is the set itself. The coloured halos are escape times. Click to dive, drag to pan, scroll to zoom, shift-click to back out.
span 3.20 · 250 iterations
The most famous
unproven shortcut
Pick a number. If it's even, halve it. If it's odd, triple it and add one. Repeat. The Collatz conjecture says you always reach 1—but no one knows. The path can climb astonishingly high before falling back down.
What to notice 27 takes 111 steps and reaches 9,232. The vertical axis is logarithmic, because the peaks are enormous compared with the finish line.
27 · 111 steps · peak 9,232
A fern from
coin flips
Don't draw a fern. Play a game instead: pick a point, roll a die, then jump halfway toward a vertex—or apply a small affine rule. Repeat tens of thousands of times and a fern condenses out of pure randomness.
What to notice Order is not always the opposite of chance; sometimes it is what chance leaves behind. Switch to the triangle to see the same trick with three vertices.
Field notes
Six ideas,
one browser tab.
This is a tiny museum with no admission fee and no gift shop. Every canvas on this page is drawn from scratch with the Canvas API. The primes are sieved, the epicycles are computed, the escape times are counted, and the fern is assembled one random jump at a time—all on your machine.
Nothing is streamed, tracked, or pre-rendered. If you find something beautiful here, it is probably a theorem in disguise. If you find a bug, it is definitely arithmetic.
“Mathematics is the art of giving the same name to different things.” — Henri Poincaré