I’ve become obsessed by what I think is a tiling of the plane by squares and equilateral triangles with the same side length. I first got an inkling of it when playing with my (almost two year old now) kid and a set of magnetic tiles. The tiling starts with six triangles organized into a hexagon, and continues from there.

Try it yourself! s to draw a square, t to draw a triangle, r to switch side, d to delete last action.