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.

This is because the image follows a basic pattern of a 4 x 4 grid - creating 16 squares at first. But even more squares emerge as two larger squares are superimposed on the centre.

So the pattern seems to collapse after the third square: 390,625 2 results in 152,587,890,625. Therefore 390,625 cannot be automorphic because the number is not completely contained in its square.

A 13-sided tile called “the hat” forms a pattern that covers an infinite plane yet it cannot repeat, making it a long-sought shape known as an “einstein.” ...

It’s been just months since researchers reported the first “einstein” — a single tile that can cover an infinite plane, but only with a pattern that never repeats (SN: 3/24/23). Now, the ...

In 1969, the British mathematician John Conway devised a beguilingly simple set of rules for creating complex behavior. His Game of Life, often referred to simply as Life, unfolds on an infinite ...

Building Facades as Beautiful, Infinite Patterns. ... a notoriously ugly building in the heart of Times Square, could be considered art, but Alexandre Jacques has a knack.