J Dean

Seconding Gynura procumbens (longevity spinach) and Gynura bicolor (Okinawa spinach) for indoor low light situations.

Plectranthus amboinicus (Cuban oregano) makes a great potted plant in indirect/indoor light and comes in at least three cultivars, two of which are handsomely variegated.

The longevity and Okinawa spinaches as well as Cuban oregano are very easy to propagate via cuttings and tolerate occasional dry spells.

Lamium galeobdolon (yellow archangel) absolutely does send out long, vigorous running vines that can root wherever they touch down, and spreads via stolons and aggressive re-seeding as well.

Houttuynia cordata (fish mint, chameleon plant) is arguably best in containers, and in low light can develop a beautiful variegated foliage. The flavor is about equal parts citrus and fish though, depending on growing conditions, so it may be limited in its culinary potential.

Eutrema japonicum (wasabi) will also grow happily in containers in full shade as long as you keep it well watered in a free draining medium and protect it from temps above about 90° F where it tends to go dormant until the rains return. Despite what you may read online, it's pretty hardy and can bounce back from heavy abuse.

I tried them last year in the Portland area and none survived outdoors without any special protection or placement. I now have about 10 eight-inch seedlings from leftover last year's seed that I planted two months ago in a passive greenhouse and they're doing great so far. I'll keep maybe five growing on in pots and try the others in different microclimates to see if I can coax some through a winter--might only need rain protection depending on the year?  The seeds are cheap and there are loads of cultivars to try so worst case it grows as an annual--and it does grow fast.  

It's also possible those ants are there to take advantage of the extra-floral nectaries, where the plant exudes nectar specifically to attract ants, who in turn protect the plants from herbivorous insects.  If you look closely at the squarish stems, each side is shaped like a little ant highway, and at the base of the petioles, where the leaf stem joins the main stem, there are a pair of little triangular stipules, each with a brownish black spot--that's the sweet spot.  If the ants are hanging out there, and not tending an aphid herd, they're actually helping protect your crop.