Multidimensional golden means

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Title: Multidimensional golden means
Author: Anderson, Peter
Abstract: 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 [2] we exploit the two-dimensional example to derive pixel permutations in order to produce computer graphics images rapidly.
Description: Presented at the Fifth International Conference on Fibonacci Numbers and their Applications, Summer, 1992. Published in: Applications of Fibonacci Numbers, Vol. 5, G. Bergum, N. A. Philippou, A. F. Horodam, ed., Kluwer, 1993, pp. 1-10.
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Date: 1993-03-18

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