EDCA as a CA composition

EDCA may be represented as a parallel bidirectional, CA composition image001  where image003  is the “ground” CA, and image005 is a set of  cellular automata, each holding a spot.

Energy cellular automata image009 share the same cellular space of dimension d with image013 , while energy expansion rule: image015 , performs the function image017 that evaluates expected energy coverage change for image019 on each spot automaton. During EDCA evolution, cells in ground image013 interact with spots in energy set image021 through Energy Incidence Criterion image023. This interaction allows spots to enable cells transitions and make cells to cause spots switch sign and move to a new location, thus causing a ground CA to perform as an Asynchronous CA. Asynchronous update pattern image025  is given by the Energy Incidence Criterion image023, where  denotes the set of cells image027 updated at time .

Transformation image042 , employed to find interacting cells and spots located on the ground and energy CA, assures the uniqueness of this solution and excludes ambiguities on the procedure of determining which cells are or aren’t enabled to change state, that is, a spot is allowed to interact with only one cell in order to contribute to its habilitation. This lack of contradictoriness guarantees the correctness of CA simulation process.

Composition approach to EDCA contributes to circumvent one of possible arguments that may be used to question its affiliation to the class of Cellular Automata, that is, the lack of strict locality on its interactions, as a cell may eventually spread its influence to an infinite zone on the cellular space, virtually “sending” a spot as far as possible.   This problem may be solved having in mind that interactions inside each component CA (ground, and those conforming energy set) are strictly local, and inter-CA interaction occurs between cells having the same coordinates in cellular space.