Joe was born and lived the first 18 years of his life in West Virgina, most notably in its highest incorporated town (pop. 600). Just before enrolling at St. John's College in Annapolis, he was able to travel around the United States for six weeks and is proud to say that he has been to 42 states and counting. After one year at St. John's, he transferred to the University of Chicago, where he worked in a neurophysiology lab and later a particle detection lab. He graduated with a major in Physics and a minor in Classical Studies, and soon after expatriated to South America. He spent three months in Chile, working on a computational investigation of the Jarzynski Equality, but he found the weather much more agreeable in Buenos Aires, Argentina, where he spent another eight months. Joe was recently recalled to the land of the free and the home of the brave to start working for Wolfram Research after informing Dr. Wolfram of a terrible premonition he had in his sleep. He occasionally maintains his own website.
Improved Visualization of Cellular Automata and Other Arrays
Finding the clearest visualization of the output of even the simplest programs is a difficult matter. Even when the input's encoding and the output's decoding are trivial, and the function of the program is well understood, the computation's detailed operation may be obscured by aspects of the system used to visualize the process. By considering a series of examples of machines whose computation is well understood, I propose to study possible visualizations of systems whose input, output, and operation are all well understood, with two goals. The first is simply to create clearer representations of these systems, as learning tools for those who are not already familiar with them. The second, and more difficult, goal is to try to discover some general principle about the visual representation of simple programs' input, output, and operation that could lead to better tools for analyzing the behavior of systems that are still poorly understood.
I'll start with developing a clearer demonstration of the prime-generating CA displayed on page 640 of A New Kind of Science, as well as an analysis of the advantages of my refinement.
Prime-Generating Cellular Automaton
Rule chosen: 214256865
Four-color, 1/2-range cellular automaton rule 214256865 with random initial conditions.