Fearless-Evolution on Boolean Landscapes: Boolean Phase Portraits Reveal a New Navigation Strategy Based on Fearful Symmetry

We present two important developments for understanding nk Boolean landscapes: First, a discrete analogue to the continuous phase portrait for analyzing Boolean landscapes and, second, an evolutionary alternative to mutation and recombination. Applications include evolution in biological systems, social networks, electrical flow on power grids, business organizations. The Curie Principle states that symmetry in causes will be seen, transformed, in effects. Using our discrete phase portrait we found that ring symmetry in network structure can be found as symmetry groups among the attractors on a Boolean landscape. The transforms which define these symmetry groups constitute a new way to move among groups of attractors (fitness peaks). A system, using only information from its current peak and a locally-generated symmetry transform, can move directly to another peak. Among the implications for theories of adaptation is our proposal of a cogent definition of fitness that goes beyond the 0 to 1 fitness metric.