Chapter 7: Mechanisms in Programs and Nature

Section 8: The Problem of Satisfying Constraints

Brillouin zones

A region in an ordinary Voronoi diagram shows where a given point is closest. One can also consider higher-order Voronoi diagrams in which each region shows where a given point is the kth closest. The total area of each region is the same for every k, but some complexity in shape is seen, though for large k they always in a sense approximate circles. 3D versions of such regions have been encountered in studies of quantum mechanical properties of crystals since the 1930s.

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From Stephen Wolfram: A New Kind of Science [citation]