<
https://kottke.org/23/03/a-potential-major-discovery-an-aperiodic-monotile>
"The authors of a new preprint paper claim that they've discovered what's
called an aperiodic monotile, a single shape that can cover a two-dimensional
space with a pattern that never repeats itself exactly. One of the authors,
Craig Kaplan, explains on Mastodon:"
How small can a set of aperiodic tiles be? The first aperiodic set had over
20000 tiles. Subsequent research lowered that number, to sets of size 92,
then 6, and then 2 in the form of the famous Penrose tiles.
Penrose's work dates back to 1974. Since then, others have constructed sets
of size 2, but nobody could find an "einstein": a single shape that tiles
the plane aperiodically. Could such a shape even exist?
Taylor and Socolar came close with their hexagonal tile. But that shape
requires additional markings or modifications to tile aperiodically, which
can't be encoded purely in its outline.
In a new paper, David Smith, Joseph Myers, Chaim Goodman-Strauss and I prove
that a polykite that we call "the hat" is an aperiodic monotile, AKA an
einstein. We finally got down to 1!
Via
Future Crunch:
<
https://futurecrunch.com/good-news-nuclear-ocean-chile-climate-change-solution/>
Share and enjoy,
*** Xanni ***
--
mailto:xanni@xanadu.net Andrew Pam
http://xanadu.com.au/ Chief Scientist, Xanadu
https://glasswings.com.au/ Partner, Glass Wings
https://sericyb.com.au/ Manager, Serious Cybernetics
