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.
Davison, J. L. "A Series and Its Associated Continued Fraction." Proc. Amer. Math. Soc.63, 29-32, 1977.Gould,
H. W.; Kim, J. B.; and Hoggatt, V. E. Jr. "Sequences Associated
with t-ary Coding of Fibonacci's Rabbits." Fib. Quart.15,
311-318, 1977.Schroeder, M. Fractals,
Chaos, Power Laws: Minutes from an Infinite Paradise. New York: W. H.
Freeman, p. 55, 1991.Sloane, N. J. A. Sequences A005203/M1539
and A005614 in "The On-Line Encyclopedia
of Integer Sequences."