Patterns Produced by Hamming Distance

length of bit sequence

3

Hamming distance h

1

In a bit sequence

b

1

b

2

…

b

n

of length

n

, each bit

b

i

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

n

2

vertices uniformly around the unit circle beginning with the vertex at

(1,0)

. 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

h

(the value of the lower control).

Some of the patterns created are remarkable.