@rainwarrior @foone I believe the innermost row - combined with the next one - is a direction encoder. So you can tell which direction the thing is spinning by comparing the phases of the two.
@TomF @foone What I realized is that a quadrature direction encoder is also the upper 2 bits of a Gray code, so it's actually the same thing.
I don't have a great intuitive reason for why it "looks" like the pattern breaks in the last row, but thinking about every column needing 1 bit to flip: the "extra" flip in the top row fills in the gap where everything else has gone to 0 to fill out the sequence of 2^6 values.