# Multidimensional golden means

 dc.contributor.author Anderson, Peter en_US dc.date.accessioned 2006-12-18T16:47:03Z en_US dc.date.available 2006-12-18T16:47:03Z en_US dc.date.issued 1993-03-18 en_US dc.identifier.citation Fifth International Conference on Fibonacci Numbers and their Applications (1992) 1-10 en_US dc.identifier.isbn 0792324919 en_US dc.identifier.uri http://hdl.handle.net/1850/3017 en_US dc.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. en_US dc.description.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. en_US dc.format.extent 163092 bytes en_US dc.format.mimetype application/pdf en_US dc.language.iso en_US en_US dc.publisher Kluwer (Springer) en_US dc.relation RIT Scholars content from RIT Digital Media Library has moved from http://ritdml.rit.edu/handle/1850/3017 to RIT Scholar Works http://scholarworks.rit.edu/other/175, please update your feeds & links! dc.subject Fibonacci numbers en_US dc.subject Monte Carlo integration en_US dc.subject Permutations en_US dc.title Multidimensional golden means en_US dc.type Proceedings en_US

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