True potato seed (TPS) is the seed produced from the fruits of flowering potato plants that have gone through sexual reproduction. So called 'seed potatoes' that are commercially available, are not really seeds, but tubers from a selected potato line - they are identical to the parent plant, since it is just vegetative propagation. There is virtually no chance of a different potato arising from this sort of propagation - indeed, that is just the point - commercial growers want reliability in the crop they are producing.
But TPS introduces genetic variability. And a quirk of most potatoes is their polyploidy. Most normal plants have pairs of chromosomes. But most 'modern' potatoes are tetraploid, they have double the number of chromosomes, which gives rise to all sorts of genetic mixing if they reproduce sexually through the flowering-cross polllination-setting seed route. This genetic mixing has the possibility of developing all sorts of interesting characteristics in the offspring.
It is possible to cross potatoes, using a similar method to tomatoes - emasculate the female parent by removing the anthers pefore they shed pollen, collect pollen from the male parent, then apply it to female parent stigma. Rather than go through all the mechanics of this, check out the information at Tom Wagner's tater-mater blog, or Rebsie Fairholm's excellent daughterofthesoil blog.
Alternatively, if you have a variety that flowers readily (not all do) and that has no self-compatibility problems (many do), and that retains its fruits to maturity, you can just see what turns up. That's what I've done.
My TPS, in this generation at least, is from self pollinated Pinkeye potatoes, derived from some certified seed tubers I purchased at my local nursery (sourced from Goodmans Seeds, if I remember correctly). There is a slight chance they have crossed with another self-propagated potato that just came up in my garden nearby, which also set a fruit, but it wasn't flowering at the same time as the Pinkeyes, so the chances of an intervariety cross is slim.
The fruits mature a bit like small hard green tomatoes, (sorry, the pic is a bit blurry) and the seed is fermented out like tomato seed - squeeze into a small container like an egg cup, leave open to the air for a few days until it ferments, then rinse the seed out in a tea strainer, and dry on a bit of paper towel.
This involves a bit of 'hilling up' in the pots, covering the lower leaves to induce tuberisation. Let the experiment continue.
Hopefully they will flower, and I'll get some more interesting colours to throw into the mix.
I've already got Purple Congo and another couple growing in the greenhouse, so I'll see what happens with their flowering phenology over autumn/winter.