A three-layered process of documentation A three-layered process of documentation: (1) First, there is the field notebook. This is where the actual numbers are recorded, together with passing observations relevant to the interpretation of these numbers. Paper is still proving more durable than electronic data. (2) The journal is a parallel record to that of the notebook—a daily account of events, thoughts, and observations. (3) Last of the three strata, then, are the publications. Traditionally, in science, these are articles in academic journals leavened with chapters in books. To be successful, a young scientist need aspire to no more than these two forms of output together with their oral versions at interminable conferences and meetings of learned societies. There came a time in my scientific development, however, when other forms of publication became important: magazines articles, and writing books. Roger Kitching, A Reflection of the Truth notetakingrecords
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