Choose shape. Mouse spreads colors. For tiles that completely cover a surface: Old idea: Fewest corners on a tile is 3, a triangle New idea: Fewest corners (vertices) on a tile is 2 The hexagon-like shape here is one of several examples
Fullscreen to see shape. For a tiling that completely covers a 2D surface, mathematicians used to say the minimum corners was 3 (a tiling of triangles). Now they say, the fewest number of corners (vertices) possible per tile is two, so long as you allow curves. In the old days, allowing curves had been considered unhelpful. Domokos, Regős, and Horváth, designed soft, two-cornered tiles from regular tilings hexagons, triangles and rectangles. The hexagonal tiles they used look like hexagons that have had two corners stretched out and the rest ground down to rounded nubs. Here, I show two versions of the hex-ish tiles.
