Information Visualization of Multi-dimensional Cellular Automata using GPU Programming

We propose a method for generating all possible rules of multi-dimension Boolean cellular automata (CA). Based on an original encoding method and the programming of graphical processor units (GPU), this method allows us to visualize the CA information flow in real-time so that emerging behaviors can be easily identified. Algorithms of first and von Neumann neighborhood second degrees are detailed with their respective fragment shaders programs. As symmetrical CA rules are especially useful in many research fields, we propose an encoding technique to automatically derive their codes; we then apply this technique to identify the 4096 possible cases for surface CA. To show the efficiency of our model a set of converging global behaviors are listed and described. In the last part of the paper we present methods for developing Moore neighborhood in two and in three dimensions. Finally we discuss issues concerning computation and the visualization of non-Boolean and higher dimension CA.