The problem with trees Many systems are organized hierarchically. The CERNDOC documentation system is an example, as is the Unix file system, and the VMS/HELP system. A tree has the practical advantage of giving every node a unique name. However, it does not allow the system to model the real world. For example, in a hierarchical HELP system such as VMS/HELP, one often gets to a lead on a tree such as: HELP COMPILER SOURCE_FORMAT PRAGMAS DEFAULTS only to find a reference to another leaf: Please see HELP COMPILER COMMAND OPTIONS DEFAULTS PRAGMAS and it is necessary to leave the system and re-enter it. What was needed was a link from one node to another, because in this case the information was not naturally organized into a tree. Tim Berners-Lee, Seeing With Fresh Eyes A City Is Not a Tree hierarchywww
Cool URIs don't change An Essay by Tim Berners-Lee www.w3.org What makes a cool URI? A cool URI is one which does not change. What sorts of URI change? URIs don't change: people change them. The User Interface of URLs www
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