Guidelines for dynamics‐based parameterization of one‐dimensional cellular automata rule spaces

Abstract

As paradigmatic complex systems, various studies have been done in the context of one-dimensional cellular automata (CA) on the definition of parameters directly obtained from their transition rule, aiming at the help they might provide to forecasting CA dynamic behavior. Out of the analysis of the most important parameters available for this end, as well as others evaluated by us, a set of guidelines is proposed that should be followed when defining a parameter of that kind. Based upon the guidelines, a critique of those parameters is made, which leads to a set of five that jointly provide a good forecasting set; two of them were drawn from the literature and three are new ones defined according to the guidelines. By using them as a heuristic in the evolutionary search for CA of a predefined computational behavior, good results have been obtained, exemplified herein by the evolutionary search for CA that perform the Synchronization Task. ᭧ 2001 John Wiley & Sons, Inc. SUMMARY C ellular automata (CA) are discrete complex systems which possess both a dynamic and a computational nature. In either case, based only upon their definition, it is not possible to forecast either their dynamic behavior, or the computation they will perform when running. However, it is possible to derive static parameters from their definition, which can then be used to estimate their dynamic behavior. This has already been done in the literature, but here we significantly extend previous efforts, by means of an analysis of the available parameters and the definition of new ones, which is achieved through the identification of a set of guidelines those parameters should abide by. The effectiveness of these guidelines are demonstrated, by using a set of five parameters drawn from them, as aids in the design of CA that should perform a predefined computational task; in the current case, such an aid represents guiding an evolutionary search for CA that perform a well-known task for one-dimensional CA, the so-called Synchronization Task.

The Intrinsic Cause-Effect Power of Discrete Dynamical Systems—From Elementary Cellular Automata to Adapting Animats

“…In Figure 5 we show the correlation between <Φ Max >, <#concepts>, and <Σφ Max > obtained from N = 5 ECA systems and three prominent measures [24], Langton's λ parameter [25], the sensitivity measure µ [26], and the Z-parameter [27]. For ECA, the λ parameter simply corresponds to the fraction of "0" or "1" outputs in the ECA rule.…”

The emergence of dynamical complexity: An exploration using elementary cellular automata

“…In order to solve the first problem, some dynamically based parametrizations of the ECA space have been proposed [7,8]. Comprehensive analysis of these parametrizations has been published [10,12]. According to these references a single parameter seems not be sufficient to forecast the dynamical behavior from the analysis of the mathematical structure of the rule.…”

Deeper Investigating Adequate Secret Key Specifications for a Variable Length Cryptographic Cellular Automata Based Model

“…Besides, it is possible to see that Subset ND returned results slightly better than Subset AA , but this improvement does not justify such reduction imposed by Rule ND . However, we decided to kept Rule ND as one of the best filters because the generalization of Neighborhood Dominance (ND) parameter from radius 2 to bigger radius is better than Absolute Activity (AA) parameter, as discussed in (Oliveira et al, 2000). Some experiments using radius 3 toggle rules specified using a filter rule based on ND are presented in (Oliveira et al, 2010c).…”