non locality of chance, a pattern in chaos

[raaaid]

i take any binary number and transfrom it into a new number by comparing each digit with the next and the last one with the first, it can be equal , e or disiqual, d

for example the number 0101 in the first transformation becomes dddd and in the second transformation eeee

well any binary number eventually transforms to all equal after a number of this transformations

check it out:



now what should be the next step?