What did we figure out?
There is a clear pattern to the widths that terminate themselves. All terminating widths can be determined by the formula 2x - 1, where x > 0 and x _ Z.
We know each pattern always terminates; since each line is directly dependent on the line above, once a single line repeats, everything recycles, and there are only a fixed number of different possible lines.
We thought there would be an easy way to predict the repetition periods mathematically.