Wolfram Computation Meets Knowledge

Wolfram Summer School


Andrew Bragdon

Summer School

Class of 2005


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).