Information Along Time-like and Space-like Paths in One-dimensional Cellular Automata

Cellular Automata offer a spacially and temporally discrete example of spacially-extended dynamical systems. These are, at minimum, two-dimensional arrays of data. Information measures are best-developed for one-dimensional sequences of data, and therefor 1-D sequences must be extracted from cellular automata if such measures are to be applied. Due to the inherent limit on the spacial extent of local state information for Elementary cellular automata for a single time step, some 1-D sequences of data can contain elements that were never in causal contact. Cellular automata were generated for the Rule 18, Rule 30, and Rule 110 cases, and 1-D sequences were extracted along paths of different velocities. Bayesian inference was utilized to estimate the entropy rate and statistical complexity of candidate ε-machines for each sequence, and these information measures were plotted against velocity.