Wolfram Computation Meets Knowledge

Wolfram Summer School


Rodrigo Obando

Summer School

Class of 2004


Rodrigo Obando was born in San José, Costa Rica. After majoring as an undergraduate in electrical engineering, he worked at several places, including computer companies, a TV station, a telephone company, and an airline. He completed his graduate work, M.E. and Ph.D., at Old Dominion University. While pursuing his degrees, Rodrigo worked with a research group at NASA Langley. There he worked in such areas as robot vision, pattern recognition, vowel recognition, fault-tolerant multicomputer operating systems, their implementation, evaluation, simulation and mathematical models. Afterwards, Rodrigo worked on a postdoctoral fellowship also at NASA Langley, where he continued his work on fault-tolerant computing.

After that he worked for several companies as a consultant and later on he started teaching information systems at Fairfield University. Rodrigo had been doing research in information visualization in the areas of distribution networks and performance evaluation of multivariate objects.

In 2002 he read Stephen Wolfram’s A New Kind of Science and found it too compelling to just sit and watch the show from the sidelines. He started working in the mapping and characterization of cellular automata rule spaces in 2003. Rodrigo presented preliminary work at the inaugural NKS 2003 conference, submitted a paper to the Journal of Complex Systems, and then presented more results at the NKS 2004 conference.

Project: Finding the Complex Rules in a 1D, k=2 Rule Space

There has been great interest in the behavior of cellular automata given a particular rule. I wish to extend some previous work performed on the elementary cellular automata (ECA) rule space to the case where the radius is 1½. This work indicates a possible way to locate the class 4 rules in a given rule space.

Researchers in cellular automata have regarded the rules as atomic in the sense that they are the smallest element in doing experiments. Instead I’d like to break the rules into primitives, even simpler elements, to investigate the rule spaces and how these simpler elements interact to produce interesting behavior. I hope this will lead to some predictive capability that can be used with other rule systems besides the cellular automata.

The crucial observation in the ECA was that the class 4 rules were made out of primitives that belong to two special subsets of the functions. There exist a set of monotone Boolean functions and its complement that are called isotone and antitone functions, respectively. One primitive of the rule belongs to the isotone set and the other to the antitone. Not all combinations from these two sets yield class 4 rules, but a structure seems to exist that holds all the class 4 rules.

The preliminary map of the spaces with k=2, r=1a needs to be completed to begin to understand how the different classes of behavior are distributed in the space. The class 4 behavior seems to be rare but nonetheless not totally unpredictable. The other classes are also of interest since the characteristics needed for each application vary widely. Other properties may also be mapped and conclusions drawn from their distribution on the rule space.

Favorite Two-Color, Radius-2 Rule

Rule chosen: Nice class 4 equivalent class {1023212796, 2146467824, 3233857731, 4026658817}