A world with pyramids Which would you choose— a world with pyramids, or a world without? Hayao Miyazaki, The Wind Rises beautyevil
To know evil For to know evil, for them, was to know it not by pure intelligence by by experience. Charles Williams, The Mind of the Maker evil
If you look for the light If you look for the light, you can often find it. But if you look for the dark, that is all you will ever see. — Uncle Iroh The Legend of Korra lightdarknessgoodnessevil
Wang tiles Wang tiles (Hao Wang, 1961) are a class of formal systems. They are modelled visually by square tiles with a color on each side. A set of such tiles is selected, and copies of the tiles are arranged side by side with matching colors, without rotating or reflecting them. The basic question about a set of Wang tiles is whether it can tile the plane or not, i.e., whether an entire infinite plane can be filled this way. The next question is whether this can be done in a periodic pattern. In 1966, Wang's student Robert Berger solved the problem in the negative. He proved that no algorithm for the problem can exist, by showing how to translate any Turing machine into a set of Wang tiles that tiles the plane if and only if the Turing machine does not halt. The undecidability of the halting problem then implies the undecidability of Wang's tiling problem. Wikipedia en.wikipedia.org Truchet TilesThe Tiling Patterns of Sebastien Truchet and the Topology of Structural Hierarchy mathalgorithms