Wolfram Computation Meets Knowledge

Wolfram Summer School


Erik Schultes

Summer School

Class of 2006


I was born into a third generation of German and Polish immigrants in Mount Clemens, Michigan. After attending public schools, I took undergraduate training in biology, geology, and mathematics at both Oakland University (Rochester, Michigan) and Humboldt State University (Arcata, California). In 1991, I attended the Santa Fe Institute’s Complex Systems Summer School and interned with Stuart Kauffman. My interests in the origin of life lead me to Bill Schopf’s laboratory in the geology program at UCLA. By 1994, I had identified RNA as an experimental system for testing elements of complexity theory pertaining to biological evolution. This revelation motivated original research in bioinformatics, the development of analytical and computational models of molecular evolution, and an informal education in molecular biology, first at the Marine Biological Laboratory at Woods Hole and then at Duke University Medical Center. In 1997, I joined the laboratory of David Bartel at the Whitehead Institute (MIT), where I used synthetic RNA constructs in vitro to probe the intrinsic structure of RNA sequence space. Many more experiments remain to be done.

Project: Phase Transitions in Cellular Automata

NKS proposes that all of nature may be described by simple rules. In the case of CA, “simple” refers to 1) a small number of cell states (K) and 2) small neighborhood sizes (N=2r+1). More-complex rules have higher K and N values but, according to the Principles of Computational Equivalence and Computational Irreducibility, these complex rules have nothing more to offer the scientist than do the simple rules. Furthermore, the space of complex rules is so large, it is no longer possible to do exhaustive searches or even know how to begin NKS experiments. But previous work by Christopher Langton in the early 1990s demonstrated that CA rule space is intrinsically organized with respect to the class of CA behavior, where class IV rules lie at a transition between classes I and II and class III. This organization becomes apparent, however, only as K and N increase to larger values. This would explain why the intrinsic organization of elementary CA rule space has not been recognized. I will survey CA behavior for 1D CA with K={2,3,4,5} and N={3,5,7}, try to locate the phase transition described by Langton, and determine if class IV rules can be systematically recovered. This is an NKS experiment applied to the usual NKS rules.

Favorite Four-Color, Radius-1/2 Rule

Rule chosen: 500

I browsed through this K=4, r=1/2 rule space, setting the initial configuration to “Black,” except for three cells, separated by “Black,” that have the states “Red,” “Green,” and “Yellow.” This configuration allowed me to analyze the dynamics of each state independently. Because of the asymmetric neighborhood, the dynamics propagated to the right. In general, it was as if these single cells were light sources, emitting “radiation.” Depending on the rule, the “radiation” from each state had different properties and propagated at different velocities. Sometimes these propagating structures collided, interacted, and created new structures. Pictured here is the highly ordered rule 500, a special case where the “Red” cell generated a Sierpinski gasket, rather than a more typical cone of light. The “Green” state immediately transitioned to the “Yellow” state, which did not propagate in space, but persisted in time.