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Wolfram Summer SchoolFounded in 2003

17th Annual Wolfram Summer School, held at Bentley University June 23–July 12, 2019 Apply Now

Alumni

Andrew Bragdon

Class of 2005

Bio

Andrew Bragdon is currently enrolled as a junior at Brown University, double-concentrating in computer science and economics. He is very interested in applying computer science to the social sciences. This summer he will work as a research assistant on a geological study of the surface of Mars using computer visualization techniques. In his spare time, he also runs a software consulting firm, Alloy Software.

Project: Turing Machine Behavior in Three Dimensions

3D Turing machines (TMs) are a largely unexplored area in the computational universe. It is the goal of this project to examine what some common "inhabitants" of this area might be. By computing a form of density on the first 30,000 two-color, two-state rules, I was able to identify interesting TMs much more quickly than by manually inspecting all 30,000 TMs. A number of groups of TMs that all exhibited similar high-level behavior were found. First and foremost, the overwhelming majority of TMs are quite uninteresting, at least outwardly, and either produce no output or an infinite sequence of repeating output. I also found a number of other classes of behavior, including examples of TMs that fill space exploders, that produce complex irregular patterns, and that reach near-equilibrium. The work has shown that definite classes of behavior exist for Turing machines in three dimensions. In addition, it has shown that a density approach to Turing machine rule-space exploration can be effective at isolating TMs of interest.

Favorite Four-Color, Nearest-Neighbor, Totalistic Rule

Rule chosen: 1635

Rule 1635--totalistic four-color automaton--HW1:

First 100 steps

Removing the banding:

As the repetitive bands are a bit distracting, I wrote some code to strip those away, leaving the image shown above (200 steps).