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Yehuda Ben-Shimol
Bio [2006]
Israel-born Yehuda teaches in the Department of Communication Systems
Engineering in the Ben-Gurion University of the Negev. In his student days
he carried out research on image processing (MSc) and relativistic
electrodynamics (PhD). Since 1998 he has been interested communication
networks and systems research and is an active author of papers in these
fields. Yehuda is also a consultant to communication and
networking companies and was the initiator of a start-up company in the
area of managed IP networks. During the NKS Summer School he was to
be seen doing Tai-Chi, just one of the internal soft martial arts he
practices. Yehuda's other interests include studying the origins of
randomness in communication networks traffic patterns, from the
perspective of finding practical applications and implementations of
Stephen Wolfram's NKS.
Project Title
Error-Correcting Cellular Automata
Project
Transmission channels are usually noisy; therefore, error correcting
codes are usually used [1,2]. Parity checking is the simplest example
of such a mechanism. Error-correcting code is needed to reconstruct
the original sequence with a limited number of errors. In this project
I'm exploring the use of simple and second-order cellular automata as
a possible mechanism for error corrections, using reversible CAs [3]
(chapter 9 pp. 435-441, notes pp. 1017-1019). Although simple reversible
rules may be configured manually (based on rotations and modular
additions), Stephen Wolfram reports many more cases (1800) for three
colors. Six out of the 1800 rules were found to have interesting
complex behavior and might be of interest for this project.
References:
- T. M. Cover and J. A. Thomas, Elements of Information Theory,
Wiley-Interscience, 1991.
- R. B. Ash, Information Theory, Dover Publications, 1990.
- S. Wolfram, A New Kind of Science, Wolfram Media, Inc., 2002.
Favorite Four-Color, Radius-1/2 Rule
Rule chosen: 3309989413
I browsed the space of all four-color automata with radius
1/2, each iteration generating 100 random images with initial value of
1. After several tens of iterations I came up with the following
interesting rules: 1696471506, 3513367967, 3309989413, 729323908,
1309766702, 319543396, and 3999440113. For these ones I generated a
series of experiments, each with a different initial value and
randomized coloring. Rule 3309989413 came up as the most appealing in
most coloring schemes. The example that is shown here is generated
with the Mathematica command ColorRules {0 ->
Hue[0.189847], 1 -> Hue[0.361915], 2 -> Hue[0.150757], 3 ->
Hue[0.96698]}.
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