Veronica filiformis Sm.
Slender Speedwell, Threadstalk Speedwell, Creeping Speedwell
Slender speedwell is a native of Turkey and the Caucasus, and it has now become naturalized in parts of Europe and North America. It appears to be rather underappreciated on the web, even though it has cool chemicals in it, in part because it has a habit of out-competing grass in lawns ... like mine. There is some evidence that some of these chemicals are natural pesticides, clearing the way for the spread of the speedwell. I found more articles on getting rid of it than I did describing it. Personally, though, I like it better than I like the lawn.
Identification: Slender speedwell generally keeps a low profile, low enough to escape the mower blades. It produces large numbers of blue-violet flowers ¼-½" (6.3-12 mm) across. Flowers have four petals, dark blue-violet stripes, and yellow-white centers.
Veronica filiformis on web.ncf.ca
Veronica filiformis on Wikipedia
Veronica filiformis on Ontario Wildflowers
Veronica filiformis at Wildflowers of Ireland
1Such as isoscutellarein 4′-methyl ether 7-O-β-(6-O-acetyl-2″-O-allosylglucoside—how cool is that?
Veronica filiformis description by Thomas H. Kent, last updated 16 Aug 2013.