Wolfram Computation Meets Knowledge

Wolfram Summer School


James Jones Rounds

Summer School

Class of 2007


James Jones Rounds has been interested in complexity and complex systems for a long time. In the past several years, he has focused his attention on neuroscience and sustainability, pertaining naturally to the complex systems of the brain and the world’s ecosystems, respectively. He finds their interaction especially interesting, and information processing has become the subject which he wants to study in greatest detail.

Currently, he is a research technician with a nanotechnology company, NanoHorizons, where he performs quality control analyses on antimicrobial fabrics and materials. He also works part time with a neuroscience laboratory at Penn State University, studying the neurochemical and behavioral consequences of genetic and dietary perturbations to the iron metabolism of rodents.

This year, he won a grant through Penn State’s Center for Sustainability to make podcasts designed to help the health care industry in Pennsylvania “go green”. He and his wife like to grow and preserve their own food and live sustainably.

Project: A Sequential Cellular Automata Model of Information Processing: A Preliminary Investigation

With these investigations I have begun to characterize the sequential 2-D Cellular Automata as they interact with images culled from the popular meme-space and the history of the image processing field.The images used include the famous ‘Lena’ photograph, a close-up of the moon’s surface, a standard “No Smoking” sign, and a seashell icon. My technique involves updating bivalent (two-color) cellular automata sequentially in a spiralling pattern, as opposed to simultaneous one-dimensional updating. This updating process occurs on a black and white, pixelated image which provides the initial condition for the rule at each step of the updating process. The sequential CA is run again on the processed image, repeatedly for up to 10 iterations. I hypothesize that the degree of complexity generated by a rule, either independently or using a background image, is not directly related to the rule’s efficacy in processing an image. In future investigations, I will investigate the condition of global control in order to assess if or how it affects 2D CA complexity and efficacy in image processing. Exhaustively investigating the various rule spaces and drawing correlations between the simplicity of initial conditions and the complexity of outcomes are the principal ways this research reflects the New Kind of Science.

Favorite Outer Totalistic Three-Color Rule

Rule chosen: 4898399

The rule I chose is 4898399, using the colors red for 0, yellow for 1, and black for 2, the asymmetrical initial condition of {0,1,0,2,0,0,0}, and looking at 200 steps.

I found this rule by using some of the filters that Paul-Jean Letourneau had provided in his lecture, but I chose not to use his background elimination filter. I wanted to look for rules that somehow established left-right symmetry despite asymmetrical initial conditions. Jamie Williams and I worked on this a little, and he developed a procedure for setting equal the first half of any row with the last half of that row (with a True or False output). However, we decided that this simple symmetry detection procedure would not find those instances in which the asymmetrical initial conditions take a little while to settle into symmetry. Also, this procedure would weed out instances in which the axis of symmetry happened to NOT occur in the center of the array.

For example, this rule is interesting to me because it develops its triangular structure after a very strange hiccup in the beginning (probably resulting from the asymmetrical initial conditions). Then, after the external frame structure reasserts its symmetry, the internal structure is quite complex (and asymmetrical), perhaps even to the degree of being Class 4. I also seem to see a conch shell on the right-hand side.

Symmetrical initial conditions also yield complex internal structure, but there is no hiccup in the beginning of the array, and the internal array is symmetrical.