Half as many people will not support half as many enterprises In a given geographical territory, half as many people will not support half as many such enterprises spaced at twice the distance. When distance inconvenience sets in, the small, the various and the personal wither away. Jane Jacobs, The Death and Life of Great American Cities densitydistancegeographybusinesseconomics
highdensityandovercrowding They hated both equally, in any case, and coupled them like ham and eggs, so that to this day housers and planners pop out the phrase as if it were one word, “highdensityandovercrowding.” Jane Jacobs, The Death and Life of Great American Cities densityurbanism
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