Surely you didn’t expect news about aperiodic tilings to appear at regular intervals? You know how it is – you wait ages for a new aperiodic monotile discovery to come along, then two come in quick succession.
In March, we covered the discovery of an aperiodic monotile. The team of authors behind that discovery have been continuing their work and this week have an even bigger announcement.
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.