Church on the Water, Hokkaido, 1985–8 At the edges of the outer walls to left and right, the slate floor is held back, creating a shadowed slot into which the concrete wall slips out of sight. Because the wall does not meet and bear upon the floor, as is usual, the relationship of the wall to the ground is uncertain, and the rippling surface of the black slate floor appears to float free of the walls, merging with the rippling surface of the water. Robert McCarter & Juhani Pallasmaa, Understanding Architecture weight
Lightness & Heaviness "Lightness is born of heaviness and heaviness of lightness, instantaneously and reciprocally, returning creation for creation, gaining strength proportionally as they gain in life, and as much more in life as they gain in motion. They destroy one another also at the same time, fulfilling a mutual vendetta, proof that lightness is created only in conjunction with heaviness, and heaviness only where lightness follows." — Leonardo da Vinci Robert McCarter & Juhani Pallasmaa, Understanding Architecture materialweight
Buttresses Buttresses, Ruskin writes, are structures against pressure: a cathedral’s walls want to fall outward, for example, pushed aside by the relentless weight of the roof. But this gravitational pressure can be stabilized by an exoskeleton: a sequence of buttresses that will prevent those walls from collapsing outward. However, Ruskin points out, there is a similar kind of pressure from the waves of the sea. Think of the curved hull of a ship, he writes, which is internally buttressed against the “crushing force” of the ocean around it. It is a kind of inside-out cathedral. Geoff Manaugh, BLDGBLOG www.bldgblog.com weightarchitecture
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