Using a variety of techniques you can create a 'crossover' between 2 genomes to breed the next generation. A simple crossover is to take the first half of one and the second half of the other and attach them together. Or any other way of combining the two to give a 'good' result, but that's the most basic way of crossover before putting the next generation into the growth chamber.
I'm developing a monster-taming/breeding game that offers dynamic breeding and the "base" type of breeding interpolates values to create the new child.
Items in-game of course can "nudge" the formula.
Doing this on the block-chain is an interesting idea a few people have suggested to me, but ultimately it didn't mesh with my idea of what the game should be.
For a better explanation, see Koza's[1] work.
[1] http://www.genetic-programming.com/johnkoza.html