A sequence which arises in the hypothetical reproduction of a population of rabbits. Let the substitution
system map 
correspond to young rabbits growing old, and 
correspond to old rabbits producing young rabbits.
Starting with 0 and iterating using string
rewriting gives the terms 1, 10, 101, 10110, 10110101, 1011010110110, .... A
recurrence plot of the limiting value of this
sequence is illustrated above.
Converted to decimal, this sequence gives 1, 2, 5, 22, 181, ... (OEIS A005203), with the 
th term given by the recurrence
relation
 |
with 
,
, and 
the 
th Fibonacci number.
The limiting sequence written as a binary fraction 
(OEIS A005614),
where 
denotes a binary number (i.e., a number written in base
2, so 
or 1), is called the rabbit constant.
