To give you a little overview over the different color variations of garter snakes, I want to show you the most common phenotypes. I want to point out up front that the color of almost all snakes, including garter and ribbon snakes, is produced by three pigments. These are: black (Melanin), red (Erythrin) and yellow (Xanthin).
As you can read in the chapter about genetics, there are recessive genes that - if they occur homozygously - lead to absence, reduction or overrun of one or several of the pigments.
Besides the colors that are a result of recessive genes there is also the possibility that conincidental new forms of appearance are produced when breeding. These cannot be explained by Mendel's laws and it's hardly possible to breed them on purpose.