The reality of the building One day I went to my study at Taliesen to sit down and rest. I picked up a little book just received from the ambassador to America from Japan. It was called The Book of Tea by Okakura Kakuzo. I wonder how many of you have read it? Well, in that little book I came upon quotations from the great Chinese poet-prophet Laotze, things he had said five hundred years before Jesus. As I turned the pages I suddenly came across this: "The reality of the building does not consist in the four walls and the roof but in the space within to be lived in..." The answer is, reality is the space within, into which you can put something. In other words, the idea. And so it is with architecture; so it is with your lives; and so it is with everything you can experience as reality. You will soon find out for yourselves if you begin to work with this principle in mind, that things will open to you...Therein lies the secret of great peace, missing in Western Civilization today. Frank Lloyd Wright, The Book of Tea space
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