Nonperiodic tiling

From Bwtm

Penrose Tiles

Steven Dutch, Natural and Applied Sciences


Rodger Penrose

Sir Roger Penrose OM FRS (born 8 August 1931) is an English mathematical physicist and Emeritus Rouse Ball Professor of Mathematics at the Mathematical Institute, University of Oxford and Emeritus Fellow of Wadham College. He has received a number of prizes and awards, including the 1988 Wolf Prize for physics which he shared with Stephen Hawking for their contribution to our understanding of the universe.[1] He is renowned for his work in mathematical physics, in particular his contributions to general relativity and cosmology. He is also a recreational mathematician and philosopher.

A Penrose tiling is a non-periodic tiling generated by an aperiodic set of prototiles named after Sir Roger Penrose, who investigated these sets in the 1970s. Because all tilings obtained with the Penrose tiles are non-periodic, Penrose tiles are considered aperiodic tiles. A Penrose tiling may be constructed so as to exhibit both reflection symmetry and fivefold rotational symmetry.

Martin Gardner

Mathematical Games, January 1977 Extraordinary nonperiodic tiling that enriches the theory of tiles By Martin Gardner

M. C. Escher

aperiodic monotile


An aperiodic monotile exists! This is probably the biggest aperiodicity news we’ll ever cover here: David Smith, Joseph Samuel Myers, Craig S. Kaplan, and Chaim Goodman-Strauss have produced a single shape which tiles the plane, and can’t be arranged to have translational symmetry.


The astonishing math behind Penrose tilings Veritasium takes a deep dive into Kepler and Penrose to examine the infinite pattern that never repeats. The overlay at about 9 minutes in is especially cool.

Penrose Tiles.

Penrose tile floors.