Re: [math-fun] Maximum orbit of an n-bit register with monotonic update rule

I don't know if this is relevant, but so-called 'Grey codes' have the property that they change only 1 bit for each 'increment'. I seem to recall that Grey codes can count through all 2^N states, although not in the usual order. Grey codes have another type of 'monotonic' property -- that, since only one bit changes on each increment, you don't need a clock to know when to sample the output of a 'counter' -- the change in any bit means that the output is available and stable. So these codes are 'self-clocking'.