Monday, July 4, 2011

"Rhombs, and wedges, and half-moons, and wings"

The line is from Paradise Regained; I found it because I was looking for pentameter lists of nouns. The first search result for "rhombs and wedges," however, is the Tilings Encyclopedia, a repository of Penrose tilings and other aperiodic (mostly substitution) tilings of the plane, such as the (new-to-me) pinwheel patterns of Radin and Conway and others, and their relatives, like this kite-domino tiling:

(The pinwheel tilings have the property that every tile appears at least once in every possible orientation.)

[PS a topic I've been paying some attention to lately is the existence of quasicrystalline, i.e., Penrose-tiling-ish, solutions to certain packing problems, which are interesting as statistical physics. For prev. coverage of this see here and here.]

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