A Toom rule that increases the thickness of sets
MetadataShow full item record
Citation (published version)P. Gacs. 1990. "A Toom rule that increases the thickness of sets." Journal of Statistical Physics, Volume 59, Issue 1-2, pp. 171 - 193 (23).
Toom's north-east-self voting cellular automaton ruleR is known to suppress small minorities. A variant,R+, is also known to turn an arbitrary initial configuration into a homogeneous one (without changing the ones that were homogeneous to start with). Here it is shown thatR+ always increases a certain property of sets called thickness. This result is intended as a step toward a proof of the fast convergence toward consensus underR+. The latter is observable experimentally, even in the presence of some noise.