metal
Dark satanic steel
When poet William Blake wrote of "dark satanic mills", he couldn't have been looking at a steel mill because there were none in 1804. Nevertheless, when I visit a steel mill, Blake's phrase always comes to mind. With the heat and the pounding noise, the dust and smoke, and the red glow against the night sky, it's hard not to see these places as infernal. And yet the process of making steel also produces some of the most hauntingly beautiful images found anywhere in the world of industry.
Grain Shapes and Other Metallurgical Applications of Topology
An Essay from A Search for Structure by Cyril Stanley Smith
The Tiling Patterns of Sebastien Truchet and the Topology of Structural Hierarchy
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.
Separation and connection in all things
Truchet's approach was more topological than geometric, and the qualitative aspects of pattern take priority over the metric ones. His principles provide a kind of metaphor for the hierarchy of separation and connection in all things.
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.
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.
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.