Paul-Jean Letourneau received an honors degree in physics from the University of British Columbia in 2003, with a specialization in biophysics and computational physics. Throughout his degree he worked for several industrial and academic laboratories around North America, where he made original theoretical and experimental contributions to real-world problems in medical imaging, protein folding, geophysical data analysis, and DNA-protein interactions.
Paul-Jean attended the 2004 NKS Summer School, where he completed a pure NKS project on elementary cellular automata with memory. He was then invited back to the 2005 Summer School as an instructor, lecturing on Mathematica programming and completing a second Summer School project based on classifying fluctuations in simple programs. Paul-Jean was an invited speaker at the 2005 Midwest NKS Conference and the NKS 2006 Wolfram Science Conference, and he returns to his role as an instructor at the 2006 Summer School.
Paul-Jean recently received a master's degree in theoretical physics from the University of Calgary, with a thesis project entitled "Statistical Mechanics of Elementary Cellular Automata with Memory."
Enumeration and Analysis of Boolean Networks
Boolean networks are an oft-used model for gene interactions, but small Boolean networks appear to never have been explicitly enumerated and studied. This project is an endeavor to enumerate and study the state transition graphs of simple Boolean networks. The project will progress in four phases.
Phase 1: Two-Input Cellular Automata
Phase 2: Two-Input Cellular Automata with Non-Local Connections
Phase 3: Two-Input Cellular Automata with Inhomogeneities
Phase 4: Two-Input Cellular Automata with Inhomogeneities and Non-Local
Rule chosen: 490694802
My favorite four-color, radius-1/2 rule number is 490,694,802. I found it doing a search for rules with interesting boundary growth from a simple initial condition. This rule supports some interesting persistent structures with at least some variety in speeds, which have some interesting interactions. The diagram shows a collision between two regions.
To find this rule, I simply found the left and right boundaries when starting from a simple initial condition, and plotted the position of the boundaries over time. I inspected the graphs of a couple of thousand randomly chosen rules, and ended up with 57 that had interesting boundaries.