Reverend Back's Abbey Floor

Reverend Back's abbey floor is a pattern constructed from the sequence of words defined by and , where denotes the reverse of a word and is a positive integer. The first few terms are then 01, 010110, 010110010110011010, .... All words are cubefree (Allouche and Shallit 2003, p. 28, Ex. 1.49). The limiting binary sequence begins 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, ... (OEIS A118006).

Plotting (mod 2), where denotes the th digit of the limiting sequence and and are positive integers, gives the pattern shown above (Wegner 1982; Siromoney and Subramanian 1983; Allouche and Shallit 2003, pp. 410-411). Note that this plot is identical to the recurrence plot (mod 2).