This is a crude tool that shows sequences of odd (1) and even (0) transistions of the initially starting with the odd numbers under 1000 and looking at the first 7 steps. The grid is formed by wrapping ever 32 numbers. Each of those parameters can be changed and then hit the button "new". If only the grid size is changed, you can hit "show" to redisplay. Also you can hover over the squares and see the starting numbers of each of the squares--the colours indicate the initial 7 steps of that number. It's interesting how the powers of two make nice bands and how the Fibonacci numbers are involved in the number of options.