Appy genes are pretty complicated and not entirely understood yet. The theory is that a horse first has to have the gene for Spotting (LP), and then on TOP of that have additional genetic coding (either an allele of the LP gene or another separate gene) for the particular pattern. There are a few sites out there covering Appaloosa genetics, but because of the lack of concrete info, I didn't put it on the reference
I taught myself for the most part, and had a lot of help from JNFerrigno who knows this stuff a lot better than I do. In terms of genetics, Appy patterns are the most complicated. Everything else is fairly straightforward lol
In terms of genetics, Homozygous means "two of the same gene" and Heterozygous means "two different genes". It's most commonly seen in relation to black and the pinto patterns.
A homozygous horse will pass on the gene no matter what. In other words, if you have a Homozygous black horse, that horse WILL pass on black to every single one of its offspring.
A heterozygous horse has a 50/50 chance of passing on the gene. Let me try to illustrate lol
A female horse is genetically XX (two X chromosomes), while a male horse is XY (one X, one Y chromosome). For the example, I'll use a female. If you have a homozygous black horse, she will carry black on BOTH X chromosomes, so XE XE. A heterozygous black only has one black, so XE Xe (small e is red, or chestnut). If you breed the homozygous mare, she has no choice but to pass on XE because that's all she has. But if you breed the heterozygous mare, she can pass on either XE or Xe to the foal.
So far there haven't been any known cases of a homozygous dominant white horse. It's believed that like Frame, it's lethal in homozygous form (the difference being that WW lethality happens so early in development that the embryo doesn't develop far enough to be born at all).
Although it could be possible, in which case the foal would also be white, or mostly white. The resulting offspring would be E-Ww. The - could be either E or e, since there's no indication of what the base colour of the WW horse is (eeWW, EeWW, or EEWW).
Just going on what I've read, the belief is that the gene might also serve another essential function beyond just coat colour. Then, the mutation that causes W also makes the second function not work right. So when you have a horse that's Ww, they have one 'defective' gene and one working gene- the working gene can pick up the slack of the one that doesn't work. But when you have WW, you have two defective genes, and no working genes, so the resulting embryo can't survive. As far as I know, that's just a theory and there hasn't been anything concrete saying that's *definitely* why, but it offers one explanation for it.