Organizing Centers in a Cellular Excitable Medium.
Arthur T. Winfree, Erik M. Winfree, and Herbert Seifert.
Excitable media support directed wave propagation that, unlike
linear waves, are directed and self-sustaining but annihilate each
other when they collide. Examples include, in one dimension, action
potential propagation along a neuron; in two dimensions, a
slow-moving fire burning across a quick-growing plain of grass
leaving a thin zone of burnt grass in its wake; in three dimensions,
the electrical-contractile waves that make heart muscle beat. The
Belousov-Zhabotinski reaction provides a simple chemical analog in
any dimension, and the Greenberg-Hastings cellular automaton
provides a simple discrete model that exhibits many of the same
qualitative behaviors. The most striking behavior of excitable
media in two dimensions is that after part of a wavefront is rubbed
out, a spiral pattern develops as the wavefront swirls around its
end. In three dimensions, one observes a wavesheet rather than a
wavefront -- and if one rubs out a hole in that wavesheet, what
develops is a remarkable three dimensional spiral. In fact there
are an infinite variety of topologically distinct three dimensional
spirals, each corresponding to the Seifert surface of a distinct
knot. We simulated two such spirals in a three dimensional
Greenberg-Hastings cellular automaton.
Physica 17D (1985), 109-115 (7 pages):
P.S. This is my first published work! My contribution, as a high
school student, was to write the program for simulating the cellular
automaton and visualizing initial conditions and the resulting three
dimensional pattern formation.
Reference details for DNA Computing conference proceedings:
DNA Based Computers: DIMACS Workshop, held
April 4, 1995 (eds Richard J. Lipton and Eric
B. Baum) American Mathematical Society, 1996.
DNA Based Computers II: DIMACS Workshop, held
June 10-12, 1996 (eds Laura F. Landweber and Eric B. Baum)
American Mathematical Society, 1998.
DNA Based Computers III: DIMACS Woskhop, held
June 23-25, 1997 (eds Harvey Rubin and David H. Wood)
American Mathematical Society, 1999.
Proceedings of the Fourth DIMACS Meeting on DNA Based
Computers, held at the University of Pennsylvania, June 16-19, 1998. (never published as a book.)
DNA Based Computers V: DIMACS Workshop, held June
14-15, 1999. (eds. Erik Winfree and David K. Gifford)
American Mathematical Society, 2000.
DNA Based Computers VI: held June
13-17, 2000. (eds. Anne Condon and Grzegorz Rozenberg)
Lecture Notes in Computer Science 2054, Springer, 2001.
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