See the previous work (well... more of a sketch really) for a technical explanation of what's going on.
This is a followup to that work. Actually, it's again more of a sketch. Part of a number of different arrangements of strings to create patterns.
If within the system one draws a grid of horizontal open strings where the information flows from left to right, with vertical ones where there flows from top to bottom crossing the horizontal lines, you apparently get something not dissimilar from a Sierpinski triangle.
When the grid has reached equilibrium I reset the color of the outer two strings manually at different times to white, black or combinations of both, to see how the information propagates.
Note btw, each bigger triangle is twice the size of the previous one, plus one extra step. In other words: the triangles are of size 1, 3, 7, 15, 31, etc.
EDIT: These are Mersenne Numbers
I'm sure it all makes perfect sense. I just haven't figured quite out why yet.