# Patterns Produced by Hamming Distance

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.

b

1

b

2

b

n

n

b

i

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).

n

2

(1,0)

h

Some of the patterns created are remarkable.