Directories aren’t surging. There isn’t this nascent directory movement fomenting - ready to take on the world. Directories aren’t trending.
But there is a certainly really sweet little directory community now. From the Marijn-inspired stuff listed in Directory Uprising to the link-sharing ‘yesterweb’ collected around sadgrl.online - or the originals at Indieseek and i.webthings.
Barnsworthburning (by Nick Trombley) is a very formidable addition to this community - a clean, multilayered design and an innovative bidirectional index.
In order that the mind may not be taxed, moreover, by the manifold and confused reading of so many such things, and in order to prevent the escape of something valuable that we have read, heard, or discovered through the process of thinking itself, it will be found very useful to entrust to notebooks...those things which seem noteworthy and striking.
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.