We investigate a geometric construction which yields periodic continued fractions and generalize it to higher dimensions. The simplest of these constructions yields a number which we call a two (or higher) dimensional golden mean, since it appears as a limit of ratios of a generalized Fibonacci sequence. Expressed as vectors, these golden points are eigenvectors of high dimensional analogues of (0 1 0 1), further justifying the appellation. Multiples of these golden points, considered "mod 1" (i.e., points on a torus), prove to be good probes for applications such as Monte Carlo integration and image processing. In  we exploit the two-dimensional example to derive pixel permutations in order to produce computer graphics images rapidly.
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Chester F. Carlson Center for Imaging Science (COS)
Anderson P.G. (1993) Multidimensional Golden Means. In: Bergum G.E., Philippou A.N., Horadam A.F. (eds) Applications of Fibonacci Numbers. Springer, Dordrecht
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