Mathy reflected binary (gray code) mindworm...

...if graycode is defined as having only one bit changed per transition, wouldn't you expect "all zeros" and "all ones" to be maximally distant from each other? Why is it a third? Is there something significant about the 2/3rd's mark then too? ... and why are 1-bit and 2-bit immune (it only starts at 3-bit)... and how does "3" come out of "binary" and "reflection" anyway!?