Wolfram Computation Meets Knowledge

Wolfram Summer School


Yehuda Ben-Shimol

Summer School

Class of 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: Error-Correcting Cellular Automata

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.


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]}.

Wolfram Summer School | Champaign, IL, USA | July 3 29–July 22, 2022