AshleyMills.com

In order to "breed" the most pretty pictures, we make their underlying functions undergo analogues of sexual and asexual reproduction.

Sexual reproduction is simulated by what is called crossover: given two function-trees a subtree from each is selected at random and then the subtrees are swapped. This is illustrated below:

Asexual reproduction is simulated by what is called mutation: given a function-tree, a node is selected at random. If it is a function node, then we replace the function with a random function taking the same arguments, and if it is a leaf then we replace the leaf with either a new random leaf or we can even grow a new subtree at that point. This is illustrated below:

Two forms of mutation are shown, in the first form, a leaf is replaced by a new subtree, and in the second a function node is changed to another function.

These are very simple ways to modify existing function-trees to produce "offspring". By using our imagination, ways different to and many variants of the above sexual and asexual reproduction methods can be conceived to produce a wide variety of offspring.