Computation at the edge of chaos: phase transitions and emergent computation
CNLS '89 Proceedings of the ninth annual international conference of the Center for Nonlinear Studies on Self-organizing, Collective, and Cooperative Phenomena in Natural and Artificial Computing Networks on Emergent computation
A new kind of science
Handbook of Graphs and Networks: From the Genome to the Internet
Handbook of Graphs and Networks: From the Genome to the Internet
Cellular Automata: A Discrete Universe
Cellular Automata: A Discrete Universe
The Structure and Dynamics of Networks: (Princeton Studies in Complexity)
The Structure and Dynamics of Networks: (Princeton Studies in Complexity)
Cell-centric heuristics for the classification of cellular automata
Parallel Computing
Handbook of Large-Scale Random Networks: Bolyai Society Mathematical Studies
Handbook of Large-Scale Random Networks: Bolyai Society Mathematical Studies
Concurrency and network disassortativity
Artificial Life
Cellular Automata and Complex Systems: Methods for Modeling Biological Phenomena
Cellular Automata and Complex Systems: Methods for Modeling Biological Phenomena
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Given two subsets A and B of nodes in a directed graph, the conduciveness of the graph from A to B is the ratio representing how many of the edges outgoing from nodes in A are incoming to nodes in B. When the graph's nodes stand for the possible solutions to certain problems of combinatorial optimization, choosing its edges appropriately has been shown to lead to conduciveness properties that provide useful insight into the performance of algorithms to solve those problems. Here we study the conduciveness of CA-rule graphs, that is, graphs whose node set is the set of all CA rules given a cell's number of possible states and neighborhood size. We consider several different edge sets interconnecting these nodes, both deterministic and random ones, and derive analytical expressions for the resulting graph's conduciveness toward rules having a fixed number of non-quiescent entries. We demonstrate that one of the random edge sets, characterized by allowing nodes to be sparsely interconnected across any Hamming distance between the corresponding rules, has the potential of providing reasonable conduciveness toward the desired rules. We conjecture that this may lie at the bottom of the best strategies known to date for discovering complex rules to solve specific problems, all of an evolutionary nature.