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We evolve network topology of an asymmetrically connected threshold network by a simple local rewiring rule: quiet nodes grow links, active nodes lose links. This leads to convergence of the average connectivity of the network towards the critical value K_c =2 in the limit of large system size N. How this principle could generate self-organization in natural complex systems is discussed for two examples: neural networks and regulatory networks in the genome.doi:10.1103/physrevlett.84.6114 pmid:10991137 fatcat:7ng67xhd2rehjd7leimzidnu34