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.
Date of creation, presentation, or exhibit
Department, Program, or Center
Chester F. Carlson Center for Imaging Science (COS)
Anderson, Peter, "Multidimensional golden means" (1993). Accessed from
RIT – Main Campus