| Search results - "bill" |
"Kissing in Motion""Kissing in Motion" shows the motion of the "shadows" of kissing spheres in a deformation pointed out by J.H. Conway and N.J.A. Sloane, following an observation of H.S.M. Coxeter. The sequence is left-right, right-left, left-right (sometimes called boustrophedon). The image accompanies "Kissing Numbers, Sphere Packings, and Some Unexpected Proofs," by Florian Pfender and Günter M. Ziegler (Notices of the American Mathematical Society, September 2004, p. 873).
--- Bill Casselman
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Coxeter groupsThis image illustrates two types of infinite Coxeter groups and algorithms involved in computation within those groups: one which generates elements of the group one by one, the "Shortlex automaton," and others, more conjectural, which seem to describe the Kazhdan-Lusztig cells of an arbitrary Coxeter group.
The illustration is described in detail and was created to accompany the article "Cells in Coxeter Groups," by Paul E. Gunnells (Notices of the American Mathematical Society, May 2006, p. 528). The explicit finite state machines required to draw the Kazhdan-Lusztig cells were supplied by Gunnells.
--- Bill Casselman
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Dyadic icosahedraThis image exhibits fanciful renderings of the dyadic icosahedra discussed in the article "The p-adic Icosahedron," by Gunther Cornelissen and Fumiharu Kato (Notices of the American Mathematical Society, August 2005, p. 720).
--- Bill Casselman
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"Ebony and Ivory," by Bill BeathBill Beath is an Australian photographer specializing in depicting nature, the countryside and architecture. His photographic work combines raditional film processes with the most modern digital techniques. His first contact with fractals was a photograph of a Nautilus shell, which led to the Fibonacci sequence, which led to his discovery of fractals and fractal art. Since then, Bill Beath has been permanently immersed in fractal art, as much as an art form as an integral part of his photographic work. For that reason this image is based on the "Fibonacci Julia" algorithm, developed by Kerry Mitchell. It shows a fascinating shape somewhere between a natural design and an exquisite man-made design. The name of the image, "Ebony and Ivory," refers to the palette used, based on elegant tones of black and white.
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