Name
Abstract | ||
|---|---|---|
Digital snowflakes are solidifying cellular automata on the triangular lattice with the property that a site having exactly one occupied neighbor always becomes occupied at the next time step. We demonstrate that each such rule fills the lattice with an asymptotic density that is independent of the initial finite set. There are some cases in which this density can be computed exactly, and others in which it can only be approximated. We also characterize when the final occupied set comes within a uniformly bounded distance of every lattice point. Other issues addressed include macroscopic dynamics and exact solvability. |
Year | DOI | Venue |
|---|---|---|
2006 | 10.1080/10586458.2006.10128978 | EXPERIMENTAL MATHEMATICS |
Keywords | Field | DocType |
asymptotic density,cellular automaton,exact solvability,growth model,macroscopic dynamics,thickness | Hexagonal lattice,Finite set,Lattice model (physics),Lattice (order),Mathematical analysis,Snowflake,Lattice gas automaton,Lattice (group),Natural density,Mathematics | Journal |
Volume | Issue | ISSN |
15.0 | 4.0 | 1058-6458 |
Citations | PageRank | References |
0 | 0.34 | 2 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Janko Gravner | 1 | 4 | 3.64 |
| David Griffeath | 2 | 13 | 2.75 |