Stippled Lines into "Dancing Ants"

This question is regarding stippled OpenGL lines. I can specify a pattern (dash-dash-dash, long-short-short, whatever) and translating my scene at subpixel levels makes the lines dance. I assume it is because the OpenGL line is recalculated so the starting point is a half-pixel off from before, so the segments of the line shift back and forth.

Anyway to fix this phenom? Moving in whole pixels is OK, but only slightly better, the ants still dance. I’d love to hear your ideas.