Leopard Complex (Lp) is what makes a horse an appaloosa pattern. It causes a malfunction that results in stopping pigment production; this makes white hair. When you only have one copy of Lp (heterozygous- Lplp), some of the pigment producing cells are able to 'overcome' the malfunction and still make pigment, hence heterozygotes have spots of color in their white. Homozygotes (LpLp) don't have enough functional protein to 'overcome' the malfunction so the pattern is solid white rather than having spots of color.
Lplp- appaloosa with spots in the white
LpLp- appaloosa with solid white
Ok, now for PATN. First remember, no matter what PATN is involved, at least one Lp is needed to be an appaloosa. What PATN does is control how big of an area the Lp malfunctioning gene affects. If there is no PATN at all, then the Lp only gets to play with the skin resulting in mottled skin, striped hooves and white sclera; these are called characteristic-only. The largest sized PATN, called PATN1, allows the malfunctioning pigment cells to have the whole body nose-to-toes. These horses are leopard spotted (Lplp) or few spots (LpLp). The less 'powerful' the PATN is, the smaller the pattern is. A blanket appaloosa has a smaller PATN than a leopard.
lplp PATN1 - not an appy
lplp PATN=small - still not an appy
lplp no PATN - You guessed it, still not an appy
Lplp PATN1 - leopard appaloosa
Lplp PATN=small - blanket appaloosa
Lplp no PATN - characteristics only
LpLp PATN1 - few spot appaloosa
LpLp PATN=small - snow cap appaloosa
LpLp no PATN - characteristics only
Think of Lp as electricity and PATN as a lightbulb. You need a both light bulb and electricity to see light.
If you have just electricity (Lp with no PATN), you still get zapped, but you don't see anything, just like a characteristic only.
If you have just a light bulb, but no electricity, well you are in the dark and the lightbulb doesn't do anything to help (PATN without Lp).
If you have a small lightbulb and only half power electricty, you get a dimly lit corner of the room (Lplp small PATN- blanket appy).
If you have a small lightbulb and full power, you have a brightly lit corner of the room (LpLp small PATN- snowcap appy).
If you have a big lightbulb and half power, the whole room is dimly lit (Lplp PATN1- leopard appy).
If you have a big lightbulb and full power, the whole room is brightly lit (LpLp PATN1- few spot).