Cellular Automata/Equivalence Classes

Introduction Stephen Wolfram was one of the first to focus on the complete set of CA rules. He observed all the rules that can be created using binary cells and a three cell neighborhood . There are such rules. The number of rules grows exponentially with the number of cell states and even faster with the neighbourhood size. This vast number of rules is a limiting factor when observing the whole set of rules. Definiton of equivalence In this definition a more formal name for rule is used, the local definition function. The local definition function is equal to the local definition function , if and ony if there exists a homomorfism of global CA states that Clustering rules or different symmetries input complement output complement reflection symmetry rotation smetry (2D) ?can be produced by reflection no it can not equivalence class Equivalence classes References Mirek Wojtowicz, Cellular Automata rules lexicon Global Dynamics http://en.wikipedia.org/wiki/Symmetries http://en.wikipedia.org/wiki/Equivalence_class http://en.wikipedia.org/wiki/Euclidean_plane_isometry about xlcau21 (22) http://groups.google.com/group/comp.theory.cell-automata/browse_frm/thread/b4596943ee04f3d6/9fffa47e715ffb7e?q=symmetry&rnum=6&hl=en#9fffa47e715ffb7e mix http://groups.google.com/group/comp.theory.cell-automata/browse_thread/thread/eedd3e963691fda2/41f376c8b51455b2?q=clusters&rnum=5&hl=en#41f376c8b51455b2 http://groups.google.com/group/comp.theory.cell-automata/browse_frm/thread/2375d42de9f86ee1?tvc=1&q=clusters&hl=en http://groups.google.com/group/comp.theory.cell-automata/browse_frm/thread/86b9db28b67edf1/c5aac90b816f8f32?q=symmetry&rnum=21&hl=en#c5aac90b816f8f32 http://groups.google.com/group/comp.theory.cell-automata/browse_frm/thread/3a24112941446717/1e809a7956a95529?q=symmetry&rnum=9&hl=en#1e809a7956a95529 http://en.wikipedia.org/wiki/Natural_isomorphism http://www.mathematics21.org/formulas-theory.html http://en.wikibooks.org/wiki/Abstract_algebra