The Tiling Patterns of Sebastien Truchet and the Topology of Structural Hierarchy

Research Paper by Cyril Stanley Smith
Screenshot of www.jstor.org on 2020-08-27 at 11.53.03 AM.png

A pattern of tiles illustrated by Douat in 1722.

A translation is given of Truchet's 1704 paper showing that an infinity of patterns can be generated by the assembly of a single half—colored tile in various orientations.

  1. ​Separation and connection in all things​
  2. ​Corpuscles of nothing and atoms of something​
  3. ​The scale of resolution determines what is seen​
  4. ​This is history​
  1. ​Truchet Tiles​
  2. ​The Sense of Order​
  3. ​The Shape of Time​
  4. ​Wang tiles​
  1. Corpuscles of nothing and atoms of something

    The structure of matter devolved ultimately into the intimate coexistence of something like corpuscles of nothing and atoms of something, segregating through the accidents of history to yield regions differing in density intimately interwoven on different scales. The experience of the world as well as human perception and analysis of any part of it is a matter of the angular scale of resolution and of the time necessary for making comparison between the different parts.

    Without such variations and without time to compare remembrances of them, nothing can be experiences.

  2. The scale of resolution determines what is seen

    The patterns of Truchet's tiles appear at first glance as variously shaped interlocked regions of black and white, the boundaries between the square tiles being submerged whenever the two regions flanking them have the same color, just as in a real floor the air or cement between the tile edges is not perceived—until one looks closely. The scale of resolution determines what is seen.

    1. ​Levels of Scale​
  3. This is history

    It is easy to see how rapidly diversity is developed by the aggregation of the simplest local choices of direction. This is history.