This is similar to the example that Stu Kauffman uses in his book on complexity. It's a geometry based on only using two amino acids and gets as complicated as 4 sites of change or 4 degrees of freedom --or, in the verbiage below, a protein exactly 4 aminos long.
This scheme can't really be used correctly for nucleotide sequences because the connectivity is all wrong, but the idea is mostly there. It works for the toy example in protein space but one quickly gets lost if he imagines 20 choices at each step of construction instead of 2. And because protein sequence depends on nucleotide sequence, it becomes important, from an evolutionary point of view, exactly what is the Hamming distances between the corresponding nucleotide sequences.
It's still a useful picture (from here).