Comparison of Evolutionary Development of Cellular Automata Using Various Representations

Abstract

A comparative study is presented regarding the evolutionary design of complex multi-state cellular automata.
 In particular, two-dimensional cellular automata will be considered in combination with pattern development problem as a~case study.
 Two techniques for the representation of transition functions for the cellular automata are proposed: a conventional table-based method and an advanced concept utilising conditionally matching rules.
 It will be shown that using a proper settings of Evolution Strategy, various working solutions can be obtained using both representations.
 Some observations from an analysis of resulting cellular automata will be presented which indicate that the behavior of the automata is totally different and depends on the representation applied.
 Specifically, the table representation exhibit a chaotic development during which a target pattern emerges at a moment.
 On the other hand, the conditional rules are able to achieve behavior that progressively constructs the target pattern which, in addition, represents a stable final state.
 Moreover, the latter method also exhibits significantly higher success rate which represents one of its advantages and proves an importance of systematic research in this area.

Evolution of Two-Dimensional Cellular Automata. New Forms of Presentation

“…There are also various approaches to the representation of evolution that use genetic algorithms and instructions [11], [18], [21], based on conditionally appropriate rules [4] based on routine evolution for complex CAs [5], evolution based on neural networks [12], [14]. There are also works devoted to the comparison of different types of evolution [6]. However, all considered evolutions show two-dimensional paintings as a sequence of two-dimensional arrays, which complicates the process of analyzing evolution for modeling various two-dimensional dynamic processes.…”