Complex Systems

Self-Replicating Sequences of Binary Numbers: The Build-Up of Complexity Download PDF

Wolfgang Banzhaf
Department of Computer Science, Dortmund University
Informatics Center Dortmund,
Joseph-von-Fraunhofer-Strasse 20, 44227 Dortmund, Germany


A recently introduced system of self-replicating sequences of binary numbers (strings) is generalized. It is extended to include strings of arbitrary length. For this purpose, first, the folding methods of strings into two-dimensional operators are expanded to include strings of arbitrary size. Second, rules of interaction between strings of different lengths are established. As a natural consequence of these interactions, changes in string length are observed. Using an effective model of length changes, the build-up of complexity as measured by the average sequence length in a string population is studied.