About cookies on this site Our websites require some cookies to function properly (required). In addition, other cookies may be used with your consent to analyze site usage, improve the user experience and for advertising. For more information, please review your options. By visiting our website, you agree to our processing of information as described in IBM’sprivacy statement. To provide a smooth navigation, your cookie preferences will be shared across the IBM web domains listed here.
Publication
Journal of Statistical Physics
Paper
A Toom rule that increases the thickness of sets
Abstract
Toom's north-east-self voting cellular automaton rule R 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 that R+ 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 under R+. The latter is observable experimentally, even in the presence of some noise. © 1990 Plenum Publishing Corporation.