This diagram is a color version of the one found in Figure 4 on page 25 of the paper "Mutation-Crossover Isomorphisms and the Construction of Discriminating Functions", together with the hypercube induced by Hamming distance outlined in light blue. It demonstrates the effect of iterated (inverse) Gray coding on the hypercube, which is very closely related to the isomorphism between Mutation and Crossover on binary string populations.
The diagram is generated by the
For the next larger (6-bit) cube, the strings starting with "0" will be isomorphic to the preceding diagram, while the subcube induced by the same strings preceded by a "1" will have this diagram.
The hope is that by studying such diagrams, and how functions are mapped onto them, we can come to a deeper understanding of how genetic algorithms work, and this in turn may lead to novel ways of exploiting the genetic operators.