Veronica Species, Thyme-leaved Speedwell, Thyme Speedwell

Not ornamental. Weedy.

Both native and introduced subspecies are widely distributed across North America.

Thymeleaf speedwell showed up in a small spot in the front lawn, where it receives morning sun. It has gradually spread till it is thick ...Read Moreenough to choke out most of the grass in the small patch where it grows. It has small oval leaves, oppositely arranged on creeping stems that root at leaf nodes. In May and June, it sends up little spikes of tiny white flowers with light purple stripes. They're just tall enough to be cut down by the mower (although perhaps it's the slight humpiness of the spot where they grow. After blooming, little heart-shaped seed pods form, which open like purses when ripe and spill tan disk-shaped seeds.

I suppose it can be called invasive, but that makes it a nice substitute for grass.