Two-dimensional tilings are admired all around the world, both for their beauty — as seen in the artistry of mosaics in cathedrals and mosques around the world — and for their utility, in walls and ...

This week, mathematicians announced the discovery of a single tile shape that produces aperiodic patterns. ... The Math of Putting Tiles Together. By Siobhan Roberts March 30, 2023.

Then, in 2023, Kaplan and collaborators stunned the mathematics world when they found the elusive einstein tile — a single shape that can fill a floor only with a never-repeating pattern ...

Copies of these two tiles can form infinitely many different patterns that go on forever, called Penrose tilings. Yet no matter how you arrange the tiles, you’ll never get a periodic repeating ...

Another take on tiling with regular polygons comes from Johannes Kepler, today best known for his discoveries about planetary motion. In 1619, he showed that even if you use more than one regular ...

Nature is full of patterns. Among them are tiling patterns, which mimic what you'd see on a tiled bathroom floor, characterized by both tiles and interfaces -- such as grout -- in between.

An “aperiodic monotile,” or einstein, is a shape that tiles an infinite flat surface in a nonrepeating pattern. The authors of a new paper called their einstein “the hat,” as it resembles ...

A new shape called an einstein has taken the math world by storm. The craggy, hat-shaped tile can cover an infinite plane with patterns that never repeat.

The first such non-repeating, or aperiodic, pattern relied on a set of 20,426 different tiles. Mathematicians wanted to know if they could drive that number down.

Nature is full of patterns. Among them are tiling patterns, which mimic what you'd see on a tiled bathroom floor, characterized by both tiles and interfaces – such as grout – in between. In ...

Such tiling patterns are found, among others, in muscle cells, zebra stripes, ... • How math people look at math, and why it works • Revisiting Make:'s weekly Math Monday column.