Where is zone 24? I wasn't aware the zones even went that high.

I live in zone 7 (NC) and use ice plant as a ground cover in the sunnier portions of my Japanese garden. It might not be very traditional, but it grows well and stays low (less than 4"). Plus it has nice flowers. I also use some ornamental grasses (Blue fescue and Pink muhly) as well as Mondo grass.

When I was in San Diego, I saw some yards that used a very low-growing groundcover that looked like moss. I'm not sure what it was called, but it would look great in a Japanese garden.

There are a lot of sedum varieties that would make nice groundcovers, particularly in your zone. My favorite is "Blue Spruce" which actually looks like little spruce needles. I've also got a small one with golden leaves but can't remember the varietal name.

If you have any shaded areas, Hakone grass makes a beautiful clumping groundcover. Mondo grass (Ophiopogon spp.) is also nice for shade.

Funny about the ice plant. Some types grow well here, but you rarely see it used for covering large areas.

You don't say whether the area is shady or sunny. If shady, I'd plant moss - it's a wonderful ground cover.

I'm in zone 8. For my sunny areas I'm using wooly thyme and also Liptinella (New Zealand Brass Buttons). One bed has a dark variety called "Platts Black", another bed has the green. It resembles tiny fern leaves growing very close together. It spreads nicely and looks good against the rocks.

Smaller leaved sedums? I've seen a tiny leaved succulent used as a ground cover that might work for you. Unhappily, I don't know the name, but I've seen it in flats at Walter Andersen's. Irish moss (Sagina) is the usual advice for warmer, drier conditions, but it still requires water from what I've read.

I have an old Japanese garden that is filled with Japanese species. It takes way too much water though and I'm trying to figure out how to revamp it with some more locally appropriate plant material, so if you have any brilliant ideas, share them please!

Notice the split z9/22 in the last post. USDA 9/Sunset 22. Most here use the USDA zones, that's why the 24 was questioned.