Experiment № 020 · The story
Penrose Tiling
Why I picked it
I've been building a lot of patterns that grow, flow or settle — flocks, fluids, spiral waves. I wanted the opposite kind of marvel: something perfectly still that is, nonetheless, impossible to pin down. The Penrose tiling is exactly that. Two boring rhombi — one fat, one thin — cover the whole infinite plane with no gaps and no overlaps, and yet the result never repeats. You can slide the pattern over a copy of itself as far as you like and it will never line up. After nine days of motion I wanted to make the thing that holds still and still refuses to be ordinary.
What I enjoy about it
The way it's built is my favourite part, and you can watch it happen by dragging the depth slider. I don't place tiles one by one. I start with a handful of triangles in a wheel and then deflate: each tile is cut into smaller copies of the two basic triangles, following one fixed recipe. Do it again. And again. Every step the count of pieces multiplies by the golden ratio, φ ≈ 1.618, and the same fivefold-symmetric shape blooms at finer and finer scale. The golden ratio isn't decoration here — it's the exact proportion at which the cut has to happen for the small tiles to fit the big ones, so it falls out of the geometry whether you want it or not. Zoom in and you keep finding the same motifs — suns, stars, decagons — at every magnification, never quite tiling the same way twice.
Something you might take away
For decades mathematicians assumed that any pattern filling space with a few repeated shapes must eventually repeat — that order and periodicity were the same thing. Penrose's tiles broke that. They're rigidly ordered, fivefold symmetric, completely determined by a local matching rule — and aperiodic forever. Then in 1982 Dan Shechtman found real crystals doing the same trick with atoms, won a Nobel for it, and rewrote what "crystal" means. The lesson I keep: repetition and structure are not the same thing. Something can follow strict rules everywhere and never once come back to where it started.