Consider the sequence defined by 
and 
, where 
denotes the reverse of a sequence 
. The first few terms are then 01, 010110, 010110010110011010,
.... All words 
are cubefree (Allouche and Shallit 2003, p. 28,
Ex. 1.49). Iterating gives the sequence 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 infinitely iterated sequence, gives the beautiful pattern shown above,
known as Reverend Back's abbey floor (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).
Cube-Free?" Bull. Eur. Assoc. Theor. Comput. Sci.,
No. 18, 120, Oct. 1982.