4 comments
After publication of Spectres, I don't know if there much interest anymore on Hats. Spectres are like Hats, but eliminate the need of reflections for tiling.<p><a href="https://cs.uwaterloo.ca/~csk/spectre/" rel="nofollow">https://cs.uwaterloo.ca/~csk/spectre/</a>
> It also complicates the practical application of the hat in some decorative contexts, where extra work would be needed to manufacture both a shape and its reflection<p>And people say that mathematical research has no practical applications
I think they are very interesting as a first step in the construction.<p>I did a write up with some app you can play with a while ago:<p><a href="https://www.nhatcher.com/post/on-hats-and-sats/" rel="nofollow">https://www.nhatcher.com/post/on-hats-and-sats/</a>
Next frontier: aperiodic tilings with irrational angles (meant, tiles having angles of x*2pi were x is irrational). Or are these proven to be impossible?<p>Because both the hats and spectres are basically subset of triangular grid. Penrose tilings are subset of regular grid, too. Can we get rid of these underlaying regular grids.
(2023)