Penrose tiling and hat tile generator
Make tilings that fill the plane but never repeat. Choose Penrose rhombs or kites and darts, a seamless Penrose-like tile, or the recently discovered “hat” — and export the result as SVG, PNG or CSS.
Open in the generator How it works
Tilings that never repeat
Most tilings repeat: shift the whole picture by some distance and it lands on itself. In the 1970s the mathematician Roger Penrose found sets of just two shapes that tile the plane only in a way that never repeats — an aperiodic tiling. Yet the pattern is far from random: it has a hidden order, with the golden ratio and five-fold symmetry all through it.
Similar five-fold order was later found in real materials called quasicrystals.
How the generator builds them
There are two classic Penrose tilings. One uses two rhombs, a thick one and a thin one; the other uses two shapes called a kite and a dart. Ornamatic grows them by repeated subdivision, so a deeper level gives smaller tiles.
Because a true Penrose tiling never repeats, it cannot be a seamless tile, so these are exported as one image. For patterns you can repeat, there is a periodic approximant: a patch of Penrose-like rhombs that repeats with a large period. Raise its order to get a longer period and a pattern closer to the real thing.
The “hat” is a single 13-sided shape found in 2023 by David Smith, Joseph Samuel Myers, Craig S. Kaplan and Chaim Goodman-Strauss. It tiles the plane only without repeating — the first single tile known to do so. Ornamatic builds it from Craig S. Kaplan’s published construction; the mirrored hats are drawn in a separate colour.
What you can adjust
- Kind — Penrose rhombs, kites and darts, a periodic approximant, or the hat.
- Subdivision depth — how small the tiles are.
- Order — for the approximant: the size of the repeat.
- Outline and rotation — the line between tiles and the angle of the pattern.
- Colours — each kind of tile gets its own colour, from any palette.
Export and use
Download the picture or the seamless tile as PNG or SVG, or copy a ready CSS background. The patterns you create are free to use, personally or commercially.
