The puzzle: Take away Triangles.
Playing with the triangles, and looking at n-gons with n >= 3, I found you always end up in some cycle ( well, unless you start with irrational numbers on the triangle’s corners ), then googling for a couple of cycle lengths, I found this integer sequence related to your triangles puzzle:
- Maximum cycle length in differentiation digraph for n-bit binary sequences.
I made this animation, showing how the cycles evolve over time for various n-gons.