Routine design When we think of bridges, it is the dramatic and monumental long spans that come to mind first, especially the lithe suspension bridges such as the Golden Gate and the pure geometric arches such as Sydney Harbour. But the majority of bridges are not such spectacular structures. Most of them are ordinary overpasses, with spans of 30 or 40 feet, carrying roadways or rails across other thoroughfares or over small streams. You see such bridges by the dozen on any drive down the Interstate. They may be lacking in glamour, but they are more representative of a bridge builder's art. The engineering and construction of girder bridges are pretty routine these days, but the bridges are not quite standard items you order from a catalogue. The girders, whether of steel or concrete, are custom-build for each bridge, then trucked to the site and hoisted into place with a crane. The designer still has scope for variation and creativity, and it shows out on the highways: some overpasses are prettier than others. Brian Hayes, Infrastructure: A Guide to the Industrial Landscape engineeringdesignautomationroutine
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