Boundary growth in one-dimensional cellular automata

Details Boundary growth in one-dimensional cellular automata Boundary growth in one-dimensional cellular automata

2012-04-10

arxiv.org/abs/1204.2172v1

Nonlinear Sciences

Cellular Automata and Lattice Gases

31 pages, 10 figures

Scientific paper

We systematically study the boundaries of one-dimensional, 2-color cellular automata depending on 4 cells, begun from simple initial conditions. We determine the exact growth rates of the boundaries that appear to be reducible. Morphic words characterize the reducible boundaries. For boundaries that appear to be irreducible, we apply curve-fitting techniques to compute an empirical growth exponent and (in the case of linear growth) a growth rate. We find that the random walk statistics of irreducible boundaries exhibit surprising regularities and suggest a threshold separating two distinct classes. Finally, we construct a cellular automaton whose growth exponent does not exist, showing that a general classification by exponent is not possible.

Affiliated with

Also associated with

No associations

Rating

Boundary growth in one-dimensional cellular automata does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Boundary growth in one-dimensional cellular automata, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Boundary growth in one-dimensional cellular automata will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-645419