I've had this game idea for a while but I have trouble finding the right keywords to research it properly.

In the end I want an animal breeding simulation, where the offsprings looks and stats are based on the parents genetics.

First I wanted to focus entirely on the fur color and pattern. So I want to make a program which I can feed the fur genetics of the mother and the genetics of the father and that then generates the genetics of the child which then also can be translated into an actual picture of the fur.

How could I do that? Where could I start?