Aperiodic tiles

Aperiodic tiling, in which shapes can fit together to create infinite patterns that never repeat, has fascinated mathematicians for decades, but until now no one knew if it could be done with just one shape

This closely follows “Tilings and Patterns” (Grünbaum and Shephard, 1987), but uses coloured diagrams rather than their monochrome ones. In some ways this is simply a catalogue of aperiodic tilings…

nakedgeometry: “ filling out the reference tables on aperiodic tile sets… #newmath #infinity ”

This is how you know you're in a mathematician's house. The bathroom floor is tiled with a Penrose tiling. (The Penrose tiling has two distinct features--first, that it's aperiodic. Second, that it's made with two basic shapes.) (There is actually one small error in this tiling. Can you spot the error?)

Mandala based on first 2 iterations of a pattern block (plus 4 pointed star) tiling. (Original)

100 Mexican Tile mix more than 30 colonial patterns similar as the image ceramic tile size: 4x4 each

Original paper: https://arxiv.org/pdf/2303.10798.pdf

Patch Penrose triangle (without rotations)