Leafy Einstein Pattern - 25 May 2024

Einstein?

Yes the recent (ish) discovery of the aperiodic monotile that I described here that I’ve been meaning to do something with. The problem I found was that trying to draw from ‘first principles’ - essentially from the angles - meant that it rapidly got out of sync and looked horrible.

When tracing a regular pattern (like an Islamic geometric one), you can have nice guidelines based on some larger scale structure. Of course, for an aperiodic tiling, there is no such larger-scale pattern. I did consider using the metatile approach, but that is fairly complex. In the end I just opted for tracing from a printout of an existing tiling.

Leafy einstein tiling with outline

Then I filled in the tiles with leaf-like drawings. Although some of these are different, I think that making them all the same 3-leaf pattern would emphasise the underlying monotile.

Then I erased the tile outline, to see what that would look like:

Leafy einstein tiling with outline

I think that looks better, although there is the danger of losing all the underlying structure. In the same vein, I don’t think connecting the leaf tiles would be a good idea.