June 24–July 13, 2018

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Wolfram Summer School

June 24–July 13, 2018
Bentley University, Waltham, MA


Joshua Schwartzstein

Class of 2003


At present, Josh is a third year student in the College of Arts and Sciences at Cornell University where he received early admission after his junior year of high school. At Cornell, Josh was selected by the University to be a College Scholar. He is currently concentrating in Mathematics, Economics and Psychology. Josh also studies Jazz Guitar and participates in both university-sponsored and student ensembles.

Project: Studying the effects of perturbations on elementary one-dimensional Cellular Automata.

This project investigates the effects of pertubations on elementary one-dimensional Cellular Automata ("CAs"). These effects are examined from "a pure NKS," as well as a social science perspective. In other words, the general evolution of the perturbed CAs is of interest as well as the pertubations' ability to produce some desired behavior. Perturbed CAs can be viewed as a model of systems affected by policies or control schemes. Through examining such CAs some inferences may be drawn as to the effectiveness and consequences of various types of policies and schemes.

Favorite Three-Color Cellular Automaton

Rule Chosen: 200013

Reason: This particular CA is interesting in that its evolution leads to five distinct regions that seemingly never interact. On the left and right borders are linearly evolving repetitive structures that encompass three more regions. The first of these--the second region from the left--contains repetitive patterns of period three. The next exhibits Class 4 behavior and contains complex structures that interact in seemingly complicated ways. The next contains a repetitive pattern that is composed of structures that take 9 steps to evolve.

Additional Information

Schwartzstein, J. "Studying the Effects of Perturbations on Elementary One-Dimensional Cellular Automata." Presentation at NKS 2004, Boston, MA, 2004. [abstract]