The thin lip of a teacup To give the building a sense of the delicacy associated with such crafts, as well as a feeling of warmth, I designed louvres from white porcelain panels, and used them to cover the outer walls. The louvres are tapered, to make their tips as fine as possible. (In fact, making tips as thin as possible is one of my key design principles: the thin lip of a teacup allows a better experience of the subtleties of tea - this is always at the forefront of my mind when I pay such close attention to edges.) Kengo Kuma, My Life as an Architect in Tokyo edges
An edge is an interface An edge is an interface between two mediums. Edges are places of varied ecology. There is hardly a sustainable traditional human settlement that is not sited on those critical junctions of two natural economies. Successful and permanent settlements have always been able to draw from the resources of at least two environments. Bill Mollison, Introduction to Permaculture As a kind of gateway edgesmedia
As a kind of gateway Historically, Japan's shrines have been built in order to worship the gods who live in the sacred mountains or seas; They don't reside in the shrine itself, but in the space beyond it. This belief that the spirits and deities exist beyond the confines of the shrine, and that the shrine itself acts not as a centre, but as a kind of gateway, is very different to the grand, imposing churches and cathedrals of Christianity. The majority of shrines are not found in the mountains or in the middle of the fields, therefore, but at the borders of mountain villages – which is to say, at what is seen as the edge of the mountains. The tori gate, marking the entrance to a shrine, indicates that there are gods on the other side of it. Kengo Kuma, My Life as an Architect in Tokyo An edge is an interfacePaths, edges, districts, nodes, landmarks religionedges
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