Apologies for the very poor photo quality - and these are the best. Pics taken early May (top) then late May (bottom), NYC USA area.

I've seen a variety of plants growing in the "soil" exposed by cracks in concrete, and in the gaps between slabs, but never like these. Unlike these relatively tall ones (guesstimate avg ~ 15"), any purple flowers which have been seen around here in similar circumstances, have always been individual, short/bushier, close to the ground, well separated plants - and were presumed to be Violets.