Boundary growth in one-dimensional cellular automata
| Title: | Boundary growth in one-dimensional cellular automata |
|---|---|
| Authors: | Brummitt, Charles D., Rowland, Eric |
| Source: | Complex Systems 21 (2012) 85-116 |
| Publication Year: | 2012 |
| Collection: | Computer Science Mathematics Nonlinear Sciences |
| Subject Terms: | Nonlinear Sciences - Cellular Automata and Lattice Gases, Computer Science - Discrete Mathematics, Mathematics - Combinatorics, 68Q80, 68R15, 82C41 |
| More Details: | 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 that a threshold separates two classes. Finally, we construct a cellular automaton whose growth exponent does not exist, showing that a strict classification by exponent is not possible. Comment: 26 pages, 11 figures |
| Document Type: | Working Paper |
| Access URL: | http://arxiv.org/abs/1204.2172 |
| Accession Number: | edsarx.1204.2172 |
| Database: | arXiv |
| Description not available. |