I don't know if these are native plants. They look like tiny daisies, are all over the lawn at English Bay right now, 2.5cm diameter, trampling height. I think they are the same plants that grow in a round area where a tree used to be at my building. It finally occurred to me to wonder what they're called. Do the purple ones have the same name as the white ones?
Bellis perennis. European. There are double flowered pink and red that look like little pompoms. Purple?
Thanks for the ID, Eric and Michael. I see common names of English daily or lawn daisy, but these didn't come up when I searched for ground cover daisy (but I used the term "lawn" in the thread title, didn't occur to me I should try the search again with that term). Maybe pink rather than purple. But single like the white ones. It's not just that the white ones start pink - in the first photo, there is an unopened white one and an about-to-open pink one. I see that there are cultivars, and that the flowers can be maroon-tinged. These photos were from today at Callister Park across from the PNE (where there is a huge amazing grove of 'Shiro-fugen' cherry trees, which Shirley will post).