Gingerbreadman Map
A 2-D piecewise linear Map defined by
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The map is chaotic in the filled region above and stable in the six hexagonal regions. Each point in the interior hexagondefined by the vertices (0, 0), (1, 0), (2, 1), (2, 2), (1, 2), and (0, 1) has an orbit with period six (except the point(1, 1), which has period 1). Orbits in the otherfive hexagonal regions circulate from one to the other. There is a unique orbit of period five, with all others having period30. The points having orbits of period five are (
, 3), (, ), (3, ), (5, 3), and (3, 5), indicated in theabove figure by the black line. However, there are infinitely many distinct periodic orbits which have an arbitrarily longperiod.
References
Devaney, R. L. ``A Piecewise Linear Model for the Zones of Instability of an Area Preserving Map.'' Physica D 10, 387-393, 1984. Peitgen, H.-O. and Saupe, D. (Eds.). ``A Chaotic Gingerbreadman.'' §3.2.3 in The Science of Fractal Images. New York: Springer-Verlag, pp. 149-150, 1988.
- Prime Circle
- Prime Cluster
- Prime Constellation
- Prime Counting Function
- Prime Cut
- Prime Decomposition
- Prime Difference Function
- Prime Diophantine Equations
- Prime Factorization
- Prime Factorization Algorithms
- Prime Factors
- Prime Field
- Prime Gaps
- Prime-Generating Polynomial
- Prime Group
- Prime Ideal
- Prime Knot
- Prime k-Tuple
- Prime k-Tuples Conjecture
- Prime k-Tuplet
- Prime Manifold
- Prime Number
- Prime Number of Measurement
- Prime Number Theorem
- Prime Pairs