They went further to suggest that there may be no such critical region. There it is argued that to find generic critical behavior one must use a general criterion for complexity in the genetic algorithm's fitness function. That a given rule exhibits critical behavior does not mean that all critical rules are closely similar to that particular rule. An example general criterion is convergence time. One may expect that on average critical rules will converge more slowly than non-critical rules.
Genetic evolution driven by convergence time indeed produces a wide variety of complex rules.
Evolution driven by an explicit fitness function favoring complex rules is but one way to obtain critical behavior. Better, from several points of view, is to use a more organic, co-evolutionary approach with an implicit fitness function. This game, inspired by the behavior of territorial birds, has been shown in the context of continuous dynamical systems to produce clear evolution toward complex behaviors. In the biological context, this game is played by birds who advertise their possession of a territory by singing a signature tune. Other birds may invade this territory under the camouflage of an imitative song.