The snowflake on the left is Marilee Rockley (yarnplayer)'s "pointed snowflake with double picots" pattern, which she generously shares on her blog.
Her pattern is written for shuttle and ball, so the rings at the tip are formed by the core thread instead of being floating rings formed the ball thread; this kinks the chains and gives a "pointy" appearance to the tips. The snowflake on the right is the same pattern, tatted with two shuttles and floating rings to show the difference.
After starching I'll likely get the same pointy effect from both as I starch heavily and block aggressively, but it's hard to be sure until I try it. Either way, it is a very cute pattern and a nice reminder that you can throw off a top-facing ring with the core thread if you're willing to kink the chain. One technical note - I'm of the "make a full double knot after each join" school, but because the tip ring is so small, this results in a noticeably lopsided ring. It looks better with the "make only the second half of the knot after the join" approach.