Parity Recurrence in Thue-Morse Sequence

initial state for heads of columns

initial state for heads of rows

step

0

1

2

3

4

5

6

7

The Thue-Morse sequence gives the parity for the sum of ones in binary numbers. It can be obtained by steps which append the binary complement of the previous step. The recurrence plot shows the mod 2 differences between the

th

x

and

th

y

terms of the sequence. The heads for rows and columns are obtained by this procedure which can start from intial values 0 or 1.