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2 Poznan University of Technology Academic Journals. Electrical Engineering

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The subclass of 2D cellular automata with one graph of connections

Porębska A.

Poznan University of Technology Academic Journals. Electrical Engineering

2011

No. 66

145--154

We describe how the rules for binary two-dimensional cellular automata with von Neumann neighborhood can be created depending on the appropriate graphs of connections. Those graphs are closely connected with configurations for which the new state of automaton cell stays one. We describe the group of rules created for the chosen symmetric graph which is the same for a few groups of configurations. We analyze how they influence the behavior of cellular automata. We observed that almost all cellular automata with one symmetric graph process the input signal in similar way. Thanks to that, in the analyses of other such subclasses of cellular automata (with other symmetric graphs of connections) we can limit ourselves to the examination of the final state achieved by only one cellular automaton with representing this group rule. It lets us make the process of searching cellular automata with the complex behavior easier.

The class of cellular automata created by the rules with the same graph of connections

Porębska A.

Poznan University of Technology Academic Journals. Electrical Engineering

2010

No. 63

7-15

One of possible class of two-dimensional cellular automata created by rules with one graph of connections is described in the paper. Basing on the computer simulation, the behaviour of cellular automata generated by rules with rotated and mirror reflected graph is tested. Close similarity between these cellular automata is observed. They process the initial signal (picture) in qualitatively the same way. Thanks to obtained results we can expect that searching of the cellular automata space in order to extract automata with interesting behaviour can be easier. It can be reduced to testing only one cellular automaton representing such class connected with one graph of connections.