Creating the tiles was simple—the first step was to find a Penrose pattern image online, which could then be used as the basis to design the 3D part in Fusion 360.

Creating the tiles was simple—the first step was to find a Penrose pattern image online, which could then be used as the basis to design the 3D part in Fusion 360.

This Penrose Tiling is one answer to a long-unsolved problem about nonperiodic tilings. A tiling is periodic if its design can be repeated by sliding, without rotating or reflecting the shapes. If ...

After Penrose described the tiling in the 1970s, the crystallographer Alan Mackay – one of the unsung polymathic savants of British science – showed in 1981 that if you imagine putting atoms at the ...

“The hat,” however, is an aperiodic tile, meaning it can still completely cover a surface without any gaps, but you can never identify any cluster that periodically repeats itself to do so.

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 ...

Penrose tilings have since entered the wild — adorning, for instance, a pedestrian street in Helsinki and the side of a transit center in San Francisco.

Smith became interested in the problem in 2016, when he launched a blog on the subject. Six years later, in late 2022, he thought he had bested Penrose in finding the einstein, so he got in touch ...

Smith became interested in the problem in 2016, when he launched a blog on the subject. Six years later, in late 2022, he thought he had bested Penrose in finding the einstein, so he got in touch ...