when i read pattern before reading the post and saw the bianary... I noticed alternating binary in the form of 43211... to what i could only assume would continue that pattern as well. "...1111, 000, 11, 0, 1, 00, 111, 0000,..."

Mirrored from one another each pair is the opposite to one another. 1 would be paired with 0... 11 paired with 00... 111 paired with 000... and continued until all of the numbers have been consumed into there proper order.