A two-dimensional piecewise linear map defined by x_(n + 1) | = | 1 - y_n + left bracketing bar x_n right bracketing bar y_(n + 1) | = | x_n. The map is chaotic in the filled region above and stable in the six hexagonal regions. Each point in the interior hexagon defined 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 other five hexagonal regions circulate from one to the other. There is a unique orbit of period five, with all others having period 30. The points having orbits of period five are (-1, 3), (-1, -1), (3, -1), (5, 3), and (3, 5), indicated in the above figure by the black line. However, there are infinitely many distinct periodic orbits which have an arbitrarily long period.
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