Abstract
Asynchronously tuned elementary cellular automata (AT-ECA) are described with respect to the relationship between active and passive updating, and that spells out the relationship between synchronous and asynchronous updating. Mutual tuning between synchronous and asynchronous updating can be interpreted as the model for dissipative structure, and that can reveal the critical property in the phase transition from order to chaos. Since asynchronous tuning easily makes behavior at the edge of chaos, the property of AT-ECA is called the unfolded edge of chaos. The computational power of AT-ECA is evaluated by the quantitative measure of computational universality and efficiency. It shows that the computational efficiency of AT-ECA is much higher than that of synchronous ECA and asynchronous ECA.
Highlights
A natural perturbed system is defined by asynchronously tuned elementary cellular automata (AT-Elementary cellular automata (ECA)) of which both passive and active updating are accepted with respect to the order of updating and neither passive nor active updating is accepted with respect to non-locality
Since Asynchronously tuned elementary cellular automata (AT-ECA) shows the critical property of the power law and complex cluster-like patterns featuring both locally periodic and chaotic interaction, it can be said that they mimic the behavior of cellular automata at the edge of chaos
Application of the device of asynchronous tuning to ECA leads to such behaviors, we call the property like the edge of chaos ubiquitously found “unfolded edge of chaos”
Summary
Schematicdiagram diagramof ofthe the adjustment adjustment of of the the passive and active rules. The bottom layer shows how the resultsof theapplication applicationof ofthe thepassive passiverule interpreted as the application of the active rule, and that leads to the update of the active rule. Each pair of squares shows a pattern generated by AT-ECA (left) and Figure 5 shows some examples of patterns generated by asynchronously tuned cellular automata (AT-ECA). Due to asynchronous class 4 like behavior, whether the original synchronous ECA are class 1, 2, or 3. The class 2 local periodic pattern generated by rule 156 or 62 shows a if the original synchronous shows the class homogeneous pattern, asynchronous tuncluster-like pattern. Even if the original synchronous ECA shows the class 1 homogeneous ing changes the behavior to the changes cluster-like pattern, asynchronous tuning thepattern.
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