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.

Date of creation, presentation, or exhibit



This is the pre-print of a paper published by Springer. The final publication is available at via

© Springer Science+Business Media Dordrecht 1993

Fifth International Conference on Fibonacci Numbers and their Applications (1992) 1-10 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. ISBN: 792324919

Note: imported from RIT’s Digital Media Library running on DSpace to RIT Scholar Works in February 2014.

Document Type

Conference Paper

Department, Program, or Center

Chester F. Carlson Center for Imaging Science (COS)


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