Response curves of deterministic and probabilistic cellular automata in one and two dimensions

One of the most important problems in the theory of cellular automata (CA) is determining the proportion of cells in a specific state after a given number of time iterations. We approach this problem using patterns in preimage sets - that is, the set of blocks which iterate to the desired output. This allows us to construct a response curve - a relationship between the proportion of cells in state 1 after niterations as a function of the initial proportion. We derive response curve formulae for many two-dimensional deterministic CA rules with L-neighbourhood. For all remaining rules, we find experimental response curves. We also use preimage sets to classify surjective rules. In the last part of the thesis, we consider a special class of one-dimensional probabilistic CA rules. We find response surface formula for these rules and experimental response surfaces for all remaining rules.

Name thesis:degree_name

M.Sc. Mathematics and Statistics

Level thesis:degree_level

Masters

Discipline thesis:degree_discipline

Faculty of Mathematics and Science

Department dc:contributor.department

Department of Mathematics

Grantor

Brock University

Year dc:date.issued

2012

Author dc:creator

• Skelton, Andrew

• Cellular automata

Handle dc:identifier.uri

http://hdl.handle.net/10464/3953

OAI identifier oai:identifier

oai:brocku.scholaris.ca:10464/3953