The Discrete Derivative Tree

The discrete derivative is founded on the recognition that two complementary strings are a partition of the infinite string of 1’s. Starting with only 00000… and 111111… we get all the binary strings as complementary pairs between the two “parents”. Starting with “0” we get the counting numbers as partitions of “1”. Growth is always to the right of the string of digits when we order them in the usual way: from left to right.