RealLife: the continuum limit of Larger Than Life cellular automata
| dc.creator | Pivato, Marcus | |
| dc.date | 2005-03-23 | |
| dc.date | 2007-02-22 | |
| dc.date.accessioned | 2026-07-07T07:47:59Z | |
| dc.date.available | 2026-07-07T07:47:59Z | |
| dc.description | Let A:={0,1}. A `cellular automaton' (CA) is a shift-commuting transformation of A^{Z^D} determined by a local rule. Likewise, a `Euclidean automaton' is a shift-commuting transformation of A^{R^D} determined by a local rule. `Larger than Life' (LtL) CA are long-range generalizations of J.H. Conway's Game of Life CA, proposed by K.M. Evans. We prove a conjecture of Evans: as their radius grows to infinity, LtL CA converge to a `continuum limit' Euclidean automaton, which we call `RealLife'. We also show that the `life forms' (fixed points, periodic orbits, and propagating structures) of LtL CA converge to life forms of RealLife. Finally we prove a number of existence results for fixed points of RealLife. | |
| dc.description | 22 pages, 3 figures. Final Version | |
| dc.identifier | https://arxiv.org/abs/math/0503504 | |
| dc.identifier | http://arxiv.org/abs/math/0503504 | |
| dc.identifier | Theoretical Computer Science, 372 (#1), March 2007, pp. 46-68 | |
| dc.identifier | doi:10.1016/j.tcs.2006.11.019 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/124347 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 37B15 (primary); 68Q80 (secondary) | |
| dc.title | RealLife: the continuum limit of Larger Than Life cellular automata | |
| dc.type | text |