spectres

At Cherry Arbor Design, my wife and I create a lot of tilings. Some allow periodic tilings. Others are aperiodic, and can’t repeat like wallpaper. Part of the appeal of aperiodic tiles is that on first encounter, it is remarkably difficult to tesselate without hitting a dead end, making them a kind of puzzle. We’ve made aperiodic Penrose tiles, Fractal Penrose tiles, the Golden B, and Ammann-Beenker tiles.

Aperiodic tilings were discovered in the 1960s. The first aperiodic tiling used over 20,000 different tile shapes. This number was reduced rapidly. By 1970, there were examples of tilings that required only two shapes. Was there a tile that only required one shape? That remained unanswered until 2023, when David Smith et al published a description of an aperiodic tile. In fact, they described several variations. One in particular has drawn attention because unlike most aperiodic tilings, it does not allow flipping the tiles over. It is called the Spectre. You can modify the edge of the Specter tile, and as long as the edge does not cross itself, it is an aperiodic monotile. So you can create your own!

We’ve written a script here that uses bezier controls to allow you to bend the edges, and create your own variation of the Spectre.