I see this plant quite frequently in Palo Alto on hellstrips between the sidewalk and the road. The thick, wavy leaves are so pretty, and then they send up small, tightly clustered purple flowers.
This plant is Limonium perezii, also known as Statice or Sea Lavender. In my opinion, the name Sea Lavender is perfect for these plants. The leaves are reminiscent of seaweed floating in the ocean.
Limonium species are mostly native to the Mediterranean area, central Asia, and, in particular, the Canary Islands, although there are a few species that are native to North America. Limonium perezii is hardy in zones 9-11 (and maybe zone 8, too, depending on the source), but it is mostly grown as an annual. The name Sea Lavender comes about because it has a high salt tolerance and likes to lives close to the ocean. At the same time, it is very drought tolerant.
The plant is evergreen, and blooms for a large portion of the year. Apparently, the “flower” (the purple part that you see) is actually the calyx, not true petals.
According to the internet, the calyx of Sea Lavender holds its color for a while, so Sea Lavender is particularly good for using as a dried flower.
Johnny’s Seeds sells Limonium sinuatum seeds:
These photos make me want to grow Sea Lavender just so I can dry the flowers to save for late winter/early spring when everything is blah outside and you can’t wait for spring to come.