3 ms·
There probably are countless others, but this is the first that we know of. And I wouldn’t know whether trivial multiples that still tile the plane non-periodi
by Someone 4y ago
There probably are countless others, but this is the first that we know of.
And I wouldn’t know whether trivial multiples that still tile the plane non-periodically exist. Once you pick a multiple, even the claim that any of these basic structures in the plane is part of the multiple you picked doesn’t seem to have an obvious, trivial (1) proof to me, let alone the additional requirement that you can find non-overlapping ones.
(1) I’m trying, likely unsuccessfully, to dodge the problem of triviality in mathematics (https://en.wikipedia.org/wiki/Triviality_(mathematics) https://en.wikipedia.org/wiki/Triviality_(mathematics)) here
- odgaus 4y agoOn their project page [1] they even mention that there is a (infinite) family of shapes >> The hat is one member of a continuous family of shapes that are all aperiodic, and that all tile the plane in the same way. [1] https://cs.uwaterloo.ca/~csk/hat/ https://cs.uwaterloo.ca/~csk/hat/