The rule is described in The Armchair Universe by A.K. Dewdney, p. 24.
It's a simple rule: the cell becomes "alive" iff the number of living neighbors
is odd. (Assuming cells are represented as 0 and 1, you can write c = sum(c,N)
neighborhood, Fredkin's rule has the fascinating property that any initial
pattern is replicated several times on a larger scale. If you're using four
neighbors (rectangular orthogonal), you get four copies of the initial starting
pattern, then 16, then 64, and so on, every so many ticks. It works for
neighborhood sizes of 6 and 8, too.
HODGE-C is a (`mostly ANSI') C language implementation of Gerhard &
Schuster's hodge-podge machine. It implements a class of cellular automata, that
resemble very closely autocatalytic chemical reactions, like for example, the
Belousov-Zhabotinskii (BZ) reaction. It's available via anonymous ftp from HODGE
John N. Rachlin <email@example.com> Charles F. Wells
<cfw2@po.CWRU.Edu> A Fraser
<A.Fraser@eee.salford.ac.uk> Rudy Rucker
The Vant rule, by Chris Langton, describes the path of an ant who starts
pointing in a certain direction. If the ant is on a non-white square it turns
the square red, rotates 90 degrees clockwise and moves one pixel in the
direction it is pointing. If it is on a red square it turns the square white,
rotates 90 degrees counterclockwise and moves one pixel in the direction it is
A generalization of Lanton's Ant can be found in Rudy Rucker, ARTIFICIAL LIFE
LAB, Waite Group Press.
There were also some articles about Lanton's Ant in Dewdney's magazine
Algorithm, and I believe there was an article in The Mathematical Intelligencer.
Langton's original article in the reference cited by Dewdney is well worth
Description: This program implements Chris Langton's cellular automaton [unk93]
requirements: This is a QBasic program that can be run on any DOS machine
with VGA graphics. It was written by Charles Wells, Department of Mathematics,
Case Western Reserve University, Cleveland, OH 44106-7058, USA.
Kendall Preston, Jr. and Michael J. B. Duff, Modern Cellular
Automata, Plenum Press, New York, 1984 (ISBN 0-306-41737-5).
These authors were mostly interested in filtering and sharpening digital
images, but there are a couple of chapters on more general automata. In
particular, they found some rules with gliders, and quite a few with
oscillators. However, nobody seems to have yet found a rule with glider guns, so
that it is hard to go on and get the other constructions which make Life
Peter Gács. Self-correcting two-dimensional arrays. In Silvio Micali,
editor, Randomness in Computation, volume 5 of Advances in
Computing Research (a scientific annual), pages 223-326. JAI Press,
Greenwich, Conn., 1989.
J. M. Greenberg, B. D. Hassard, and S. P. Hastings. Pattern formation and
periodic structures in systems modelled by reaction-diffusion equations.
Bulletin of the American Mathematical Society, 84:1296-1327, 1978.