A tiling is periodic if it admits translations in at least two non-parallel directions. A collection of tiles is aperiodic if the collection tiles the plane, but never in a periodic fashion.
Wang's conjecture: No aperiodic set exists. The conjecture was proved false by Berger in 1966.
Berger: 20,426 Wang tiles, 1966, later reduced to 104
Knuth: 92, 1968
Robinson: 35, 1971
Penrose: 34
Amman: 16, 1978
Kulik: 13, 1996
Theorem (Robinson): No periodic set of 4 Wang tiles exists.
In 1971 Robinson created this aperiodic set of 6 tiles.
These are not Wang tiles.
If you try to make a periodic pattern, the tiles won't let you:
