The original version of this story appeared in Quanta Magazine. If you want to tile a bathroom floor, square tiles are the simplest option—they fit together without any gaps in a grid pattern that can ...

The Penrose tiling pattern is a type of quasicrystal, which means that it has an ordered yet never-repeating structure. The pattern, composed of two shapes, is a 2D projection of a 5D square lattice.

Watch for the patterns created as the circles move across each other. Those patterns, created by two sets of lines offset from each other, are called moiré (pronounced mwar-AY) effects. As optical ...

Ah, tiles. You can get square ones, and do a grid, or you can get fancier shapes and do something altogether more complex. By and large though, whatever pattern you choose, it will normally end up ...

Ah, tiles. You can get square ones, and do a grid, or you can get fancier shapes and do something altogether more complex. By and large though, whatever pattern you choose, it will normally end up ...

If you want to tile a bathroom floor, square tiles are the simplest option — they fit together without any gaps in a grid pattern that can continue indefinitely. That square grid has a property shared ...