The ability to make custom patterns is quite helpful but learning how to make patterns that repeat seamlessly in Illustrator makes it even better. Patterns that will show where the edges repeat may ...

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 ...

Is it possible to tile a surface with a single shape in such a way that the pattern never repeats itself? In 2022, a mathematical solution to this 'Einstein problem' was discovered for the first time.

Remember the graph paper you used at school, the kind that’s covered with tiny squares? It’s the perfect illustration of what mathematicians call a “periodic tiling of space”, with shapes covering an ...

Conventional crystals are materials in which atoms arrange themselves in repeating spatial patterns. Time crystals, on the other hand, are phases of matter characterized by repeating motions over time ...

IT may not be generally known that the Theorem of Pythagoras, Euclid I. 47, is closely connected with the Theory of Repeating Patterns in space of two dimensions. The simplest proof by dissection of ...

SOME correspondence appeared in NATURE in 1938 about the phenomenon described by Brewster 1, which is obtained by focusing on a surface covered by a repeating pattern while converging on a point ...