Toadflax, or Dwarf Kenilworth Ivy
Cymbalaria aequitriloba (formerlyLinaria aequitriloba) is such a tiny groundcover even moss can appear tall beside it. Some discriptions say it gets one inch tall, but one discription said it grows "0 to 3 inches." Zero inches tall isn't all that absurd. In our garden, it isn't even a full fourth-inch tall. It is rarely offered by nurseries because it might be mistaken for a bit of volunteer moss.
Granny Artemis planted a little start of this alongside the staircase to the lower street, where it is situated underneath Sword Ferns. It's a good thing it's close within hand's reach, as it frequently needs leaf litter brushed from it.
This little toadflax is native of Spain & southern Europe. It is sometimes called Dwarf Kenilworth Ivy, due to the three-lobed ivy-like shape of the small leaves. The non-dwarf variety is C. muralis & is more obviously a trailing vine.
Dwarf Kenilworth is evergreen, but not very cold-hardy. Though it does okay at about 15 to 20 degrees or a little cooler, a severe cold-snap could take it by surprise & do it in.
It is also sensitive to heat & has to be protected from much sun. We rarely have extremely high or low temperatures, so our little patch of it has done fine for three years, though it has not spread much at all. In perfect conditions it will self-seed & slowly cover over the ground, so I guess our conditions aren't perfect since it is not just slow growing but extremely slow growing.
Dwarf Kenilworth Ivy has purple & white snapdragon-like flowers. It'll have an occasional surprise flower early in spring or even in late winter, but does not dust itself all over with blooms until May. It will continue to have flowers on it from time to time right up to first frost in Autumn.