Patterns Produced by Hamming Distance

In a bit sequence of length , each bit is either 0 or 1. The Hamming distance between two bit sequences is the number of bits in which they differ.
This Demonstration constructs a graph by placing vertices uniformly around the unit circle beginning with the vertex at . List the bit sequences in base-2 order at the vertices going counterclockwise. Two vertices are connected with an edge if the Hamming distance between their corresponding bit sequences is (the value of the lower control).
Some of the patterns created are remarkable.

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