hi Todd,
what do you need to calculate a cell in a diagonal? The previous cell in that diagonal and two cells from the previous two diagonals. This enables one to define diagonals recursively. For diagonals from the right, the recursive definition leads to a simple picture: The previous two diagonals are combined with OR and the resulting values are combined with XOR - basically a summation over the combination up to the cell you need. It is this summation modulo 2 that causes the period doubling. I show that it will either double the basic period of the combination or leave it untouched. But combining the previous two diagonals with OR may decrease the basic period - so I also show that this cannot happen in diagonals from the right.
This is what may be new - I don't know. The rest should be well known stuff - maybe looked at from a different viewpoint. Using a richter structure by replacing A OR B with A+B+A*B did not yield any really interesting results IMO but I left it in the article because it was my starting point.
