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algorithm applications automata networks automaton average basin of attraction behavior binary biological boolean automata boolean functions boolean networks calculate cell cellular automata chapter complex systems components connectivity corresponds decimal code defined depends described disordered systems distance equation evolution example ferromagnetism fixed points genomes given Hamming distance Hebb rule Hopfield model Hopfield networks initial conditions initial configuration input configuration interactions invariant large number lattice limit cycle linear loop machine magnetic matrix method mutations neighbors neurons nodes number of attractors number of automata number of references numerical simulations observed obtained organisms oscillating output particles patterns perceptron period phase transition pixels populations possible probabilistic probabilistic automata probability problem processing processors random randomly regime represented scaling laws shown in figure signal simulated annealing species spin glasses structure subnetworks symmetrical synaptic weights temperature threshold automata tions transition function truth table units variables vector zero