Lithops belongs to the Aizoaceae family, and everything I've seen from this family is from Southern Africa. I love Lithops and they need a lot of sun to grow which can be challenging in Oregon. I've had this guy for about a year (which is pretty good because I killed the first one). What I do with all the members of Aizoaceae (which is working where I live) is to keep them in the sunniest window I have from early fall to early spring (which is when they grow and need the most water), then put them outside in the sunniest spot the other half of the year. I've found that I'm having to water them quite a bit right now because it's been so hot and dry.
Anyway, this Lithops doubled in size since I got it:
It used to be just one half. What happens is two grow inside one of them and apparently use the nutrients from the old one which starts to shrivel up around the new ones until it's a papery skin (see to the right of the plant). Therefore, if all goes well this winter, I should have four of these cute little guys next year!
Oh, and these plants need a deep pot because they have a tap-root, and they (and the "split rock" from this post) need a lighter, more well-draining soil than typical succulents!
It's Famers' Market day, yay!