an aperiodic monotile · n = 1
In 2023 a single shape was found that tiles the plane, but only aperiodically: the pattern never repeats. Its curved edges make the matching rule physical: a bump only nests into a dent. Smith, Myers, Kaplan & Goodman-Strauss →
guided only offers placements that provably extend to a perfect, hole-free tiling. They are checked against a 4400-tile master patch built from the Spectre's substitution rules. worlds counts how many places in that master tiling your patch could still be: every choice you make destroys worlds, which is the information your figure encodes. local offers anything that merely fits its neighbours. Watch worlds hit zero when you paint yourself out of the true tiling. free has no rules at all.
Read the full explanation of the algorithm and the mathematics behind it →
| place | move the ghost near an edge; it snaps to valid spots. Click to commit |
| paint | in guided mode, hold the button and sweep: every valid tile along your path is placed for you |
| rotate | right-drag, quick right-click, R, or the ⟳ button |
| erase | switch to erase, then click tiles |
| colors | 🎨 picks a brush: new tiles take that color, clicking a tile repaints it; "auto colors" returns to the palette |
| pan / zoom | middle-drag (one-finger drag on touch) / scroll to zoom |
| undo | Cmd/Ctrl+Z |
| auto | tiles a disc around your patch by itself, outside edge first, then inward |
| replay | ▶ plays your build back like sheet music (loops, scrubbable). Click while paused to keep building from that moment |
| save | copy a replay link, or publish your shape by name to the public gallery |
| browse | load anyone's published shape from the gallery |
Everything is open source, MIT licensed: github.com/RemiFabre/spectre-playground
click anywhere to close