Depends on what you mean by pattern. Color patterns like the spots on a cow are randomized, but specific kinds of snakes(piebalds, clowns, etc.) are genetic.
Eh, let me explain that better.
Breeding two pieds will get you a pied, but his or her pattern will not resemble his or he parents. Even if you were to clone an animal, the pigment cells that make up their coloring arrange themselves while the animal develops in utero(or egg), so an animal with spots or stripes will have a different arrangement than their parents.