Schema Redescription in Cellular Automata: Revisiting Emergence in Complex Systems

Manuel Marques-Pita1,2,3 and Luis M. Rocha1,3

1 School of Informatics and Computing, Indiana University, 919 East Tenth Street, Bloomington IN 47408, USA
2Portland State University
3FLAD Computational Biology Collaboratorium, Instituto Gulbenkian de Ciencia, Portugal

Citation: M. Marques-Pita and L.M. Rocha [2011]. "Schema Redescription in Cellular Automata: Revisiting Emergence in Complex Systems". In: The 2011 IEEE Symposium on Artificial Life, at the IEEE Symposium Series on Computational Intelligence 2011. April 11 15, 201, Paris, France,. IEEE Press, pp: 233-240.

The pre-print is also available from the Due to mathematical notation and graphics, only the abstract is presented here.


We present a method to eliminate redundancy in the transition tables of Boolean automata: schema redescription with two symbols. One symbol is used to capture redundancy of individual input variables, and another to capture permutability in sets of input variables: fully characterizing the canalization present in Boolean functions. Two-symbol schemata explain aspects of the behaviour of automata networks that the characterization of their emergent patterns does not capture. We use our method to compare two well-known cellular automata for the density classification task: the human engineered CA GKL, and another obtained via genetic programming (GP). We show that despite having very different collective behaviour, these rules are very similar. Indeed, GKL is a special case of GP. Therefore, we demonstrate that it is more feasible to compare cellular automata via schema redescriptions of their rules, than by looking at their emergent behaviour, leading us to question the tendency in complexity research to pay much more attention to emergent patterns than to local interactions.

Keywords:Cellular Automata, Emergent Computation, Collective Behavior, Self-Organization; Dynamics, Canalization, Complex Networks, Artificial Life, Density Classification Task.

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Last Modified: March 21, 2011