First of all, I'd suggest you plant a perennial (purple alyssum is an annual).
It's a tough environment. It will be soggy for half the year as its root zone is a low spot that will receive runoff from the flagstones. It will also bake in the summer and the stones will amplify the ambient air temperature. Mentha requienii is one of the standards for flagstone fill, but will probably need summer irrigation in your case. There are also various small sedums and other more drought-tolerant choices. I'd check out some of the options at Stepables.com.

Myself, I like creeping thyme, but here is a website that specializes in just what you are looking for--plants that can be walked on.

Carla in Sac

Here is a link that might be useful: http://www.stepables.com/1/Plants.html

I use a combination of plants, since nothing does well all year. I have dichondra, baby tears, woolly thyme, and elfin thyme in various spots. Some get sprinkler overspray, some has to depend on occasional hose water. You can also try violets. They spread very well in shady dry conditions.
Renee

See if Dymondia margaretae is hardy in your 15. The sun in the summer should be enough to carry it through the less sunny winter. You would not have to water it at all in the rainy season and a soaking twice a month in summer would be plenty. A fine little groundcover.

Thanks for advise guys! I used stepable.com and narrowed it down to 3 candidates:

Corsica Mint {{gwi:563204}}, or Magic Carpet Thyme {{gwi:563207}}, or Red Creeping Thyme {{gwi:563210}}.

The objective now is to find an affordable way to fill about 100' or 1200" of linear space between gaps. Most ground covers require planting every 6-8" or so. At 8", that translates into 150 plants or 25 6-packs, @$4/pack = $100. Are there cheaper way to do it? Are they hard to start by seeds?

I bought seeds of creeping thyme from this site for $2.50, with the intention of doing what you are planning. (I have not gotten around to planting them yet, though!) Much cheaper, and they might be ready to go by next spring if you--or I :)--plant now.

Carla in Sac

Here is a link that might be useful: Thyme Garden Herb Company

Hey Carla,

This is a pic of red creeping thyme on pink flagstone {{gwi:563212}}.
My flagstone are much large but same color. In fact, the visual effect would be very similar to the purple alyssum that I used this year.

I think the corsican mint spreads.
Renee

Corsican mint vs creeping thyme. Which one uses less water and which one grow faster?

This may not be to your taste, but there's a native perennial lippia (Phyla nodiflora) that does very well between stepping stones. I've never seen it available for sale, but you may already have it as a lawn weed, or if you keep an eye out for it during its blooming season, you might easily spot it between the cracks of a sidewalk near you. I found some among the weeds along an asphalt bike path a few blocks from our home and transplanted it into our yard last spring. It does (obviously) have weedy tendencies (I now have two patches of it across the yard from where I planted it, in addition to to the patch that I actually planted), but so do purple alyssum and really most plants that do well between stepping stones. If it shows up somewhere you don't want it, it's easy to pull. Most importantly, to my mind, it's quite pretty, remains in bloom for about six months (May through October), stays absolutely flat to the ground, and seems perfectly happy to bake in dry, cracked clay all summer but sit underwater for weeks in the winter. I'm expecting mine to die back to its roots for a short time in winter (though it's shown no sign of doing so yet) - but in places with milder winters, such as the Bay Area, it's evergreen.

Here is a link that might be useful: CalPhotos: Phyla nodiflora

I have been happy with woolly thyme as it will soon fill in and looks good all year. What ever you decide buy it by the flat. You will get up to 50 plants per flat and most nurseries will be glad to order it for you, many will have it as a stock item. Al