Pure Chance Genetics

Having the set $\cal{G}$ $^{\emptyset}$ as assumed to be different from the 'goal' set $\cal{G}$$^{*}$ one has to organize the function $\gamma$ as a sequence of substitutions where every substitution should be done by 'pure chance'.

Here we have to distinguish two cases:

1. Pure chance with no inheritance
2. Pure chance with inheritance

Even if there is no fitness feedback through $\Sigma^{*}$ true genetic systems are not completely at random because of inheritance. Inheritance functions like a kind of a 'memory' holding back the information of the last generation and allowing either only combinations of given genomes (crossover) or allowing limited local changes (mutation) for the next generation of offspring.