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Rabbit Sequence

A Sequence which arises in the hypothetical reproduction of a population of rabbits. Let the Substitution Map $0\to 1$ correspond to young rabbits growing old, and $1\to 10$ correspond to old rabbits producing young rabbits. Starting with 0 and iterating using String Rewriting gives the terms 1, 10, 101, 10110, 10110101, 1011010110110, .... The limiting sequence written as a Binary Fraction $0.1011010110110\ldots_2$ (Sloane's A005614), where $b_2$ denotes a Binary number (a number in base-2) is called the Rabbit Constant.

See also Rabbit Constant, Thue-Morse Sequence


Schroeder, M. Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise. New York: W. H. Freeman, p. 55, 1991.

Sloane, N. J. A. Sequence A005614 in ``The On-Line Version of the Encyclopedia of Integer Sequences.''

© 1996-9 Eric W. Weisstein