This really only works on a non periodic developable surface. A defining feature of aperiodic tilings is that they can’t be translated onto a copy of themselves.
Here’s a definition with a much larger patch, showing how the mapping can be used to apply other geometry onto the tile.
Aperiodic_Monotile2.gh (567.3 KB)
These patterns can help reveal some of the complexity of the arrangement.
I find it amazing how much structure can come from such a simple shape.
