[rini17]

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?

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.

[zem]

it feels like it would be hard for those to tile at all, let alone aperiodially

[WCSTombs]

Not really, since you can take a standard square tiling and apply a random shear transformation to it. With probability 1, you get a tiling of parallelograms with irrational angles.

[ganzuul]

Spiral out and keep going?