This app is based on the “Conway Criterion,” a set of conditions for a shape (a tile) to fill the plane with its copies simply by turning the tile 180° repeatedly about certain points on the edges of the tile.

John Horton Conway (1937-2020) was a mathematician who made important contributions to many fields of mathematics; you can read more about him here. He discovered this criterion while trying to determine which of the 108 heptomino tiles (made up of 7 identical squares stuck together at their edges) could tile the plane. If a tile satisfied the conditions of his criterion, it was guaranteed to tile the plane. The Conway's Magical Pen app allows you to create your own original tiles that satisfy the Conway criterion; they are called Conway tiles. You can download the article Will it tile? (PDF) by Doris Schattschneider that explains this criterion.



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