Christie L. Gilbert, Joseph D. Kolesar, Clifford A. Reiter, and John D. Storey, Function Digraphs of Quadratic Maps Modulo p, The Fibonacci Quarterly, 39 1 (2001) 32-49.

This paper investigates the structure of the digraphs that result from the iteration of quadratic maps x2 + c modulo a prime p. Bounds on the number of elements of cycles of a given length are given recursively and empirical comparisons are made with quasiquadratic maps. In addition to the rich structure for x2, there is rich structure for x2 - 2. This structure involves cycles with a single leaf attached to each cycle and other cycles with binary trees attached to the cycle. Those features are investigated via relations that relate geometric position in the digraph with both additive and multiplicative arithmetic.

See Also: · Paper Preprint · There is an established and growing literature related to this subject. A motivating reference was: E. L. Blanton, Jr, S. P. Hurd and J. S. McCranie, On a Digraph defined by squaring modulo n, The Fibonacci Quarterly 30 4 (1992) 322-334. · An investigation of digraphs from powers xn mod p appears in [nt_1996].