Pod colour and shape were a couple of the characteristics studied by Mendel. There is a brief description along with some photos on the JI site, here.
Chlorophyll is either switched on or off by the dominant gene Gp, giving either green (Gp) or yellow (gp) pods.
|A young Golden Podded|
But purple is a different matter. You need one gene to turn on anthcyanin production (A). Then other genes turn on its distribution across the plant, that is, where it gets expressed. To get full purple pods, you need the dominant genes Pu and Pur. Other genes give purple splodges in the leaf axils, purple flowers and purple or brown in the seed coats.
Fibre in the pods, or more correctly lack of fibre in the pods is what makes a snowpea a snowpea. Fibre is controlled by two dominant genes, V and P. V makes the pod relatively smooth, v makes the pod clasp the contained peas, giving a lumpy pod.
So to get a purple podded snow pea from a purple podded pea and a snow pea cross, you need to get three dominant genes for purple pod combining with two recessive genes for low fibre. To get this in one go from a cross if the parents don't share any of these genes is a tall order - 9/4096, or about 1 in 500.
If you want to include any other characterisitcs - say dwarf growth form, double flowers (gives more production) or disease resistance, unless both parents have that gene, the chances diminish considerably.
Powdery mildew is a bit of a problem where I garden, so that gene (or genes, as it turns out) would be good.
I can reduce the odds if I can use parents that share some of these genes. But there are no purple podded low fibre peas, all of the purple podded peas I have are all tall, single flowered, and they all seem to be subject to powdery mildew. One variety (PP Lost Seed Company) is a bit earlier than the others so I have used it for a number of my early crosses - maybe it will confer earliness to its offspring.
On the snow pea side, Yakumo has purple flowers, showing it carries the A gene, but is tall, subject to disease, and in my observations, is only single flowered. But since it carries A, if I did a cross to a purple podded, I would be assured that all the offspring would carry A, improving my chances of getting a PPSP by four.
Melting Mammoth has double flowers, but probably doesn't carry the A gene. It is also subject to powdery.
Delta Louisa is a dwarf, has purple flowers (A), is double flowered and is powdery mildew resistant - a good candidate for one of the parents.
I'm also growing Oregon Spring - a double flowered white dwarf, which also looks like it is powdery resistant, and Swiss Giant, which I haven't grown before, but which looks to be double flowered and purple flowered, another good candidate for parenthood. I will have to check for disease resistance as the season progresses.