Zoning for diversity As production becomes increasingly clean and knowledge-based, as our urban economies tip dramatically to service industries, as racism and ethnic animosities ebb, and as the model of mixed use becomes more and more persuasive and visible, cities are in a position to dramatically rethink zoning as a medium for leveraging and usefully complicating difference, rather than simply isolating it. Michael Sorkin, 20 Minutes in Manhattan zoningrace
The greatest flaw in city zoning Raskin, in his essay on variety, suggested that the greatest flaw in city zoning is that it permits monotony. I think this is correct. Perhaps the next greatest flaw is that it ignores scale of use, where this is an important consideration, or confuses it with kind of use. Jane Jacobs, The Death and Life of Great American Cities zoningmonotonyscale
The air doesn't know about zoning boundaries Work uses suggest another bugaboo: reeking smokestacks and flying ash. Of course reeking smokestacks and flying ash are harmful, but it does not follow that intensive city manufacturing (most of which produces no such nasty by-products) or other work uses must be segregated from dwellings. Indeed, the notion that reek or fumes are to be combated by zoning and land-sorting classifications at all is ridiculous. The air doesn’t know about zoning boundaries. Regulations specifically aimed at the smoke or the reek itself are to the point. Jane Jacobs, The Death and Life of Great American Cities zoningregulationsseparation
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