Given an interval or a higher dimensional block of points, that may be either continuous or discrete, how can we probe that set in a smooth manner, visiting all its regions without slighting some and overprobing others? The method should be easy to program, to understand, and to run efficiently. We investigate a method of visiting the pixels (the elements of a rectangular matrix) and the points in the real unit cube based on an arithmetic progression with wrap-around (modular arithmetic). For appropriate choices of parameters, choices that generalize Fibonacci numbers and the golden mean, we find equidistributed collections of pixels or points, respectively. We illustrate this equidistributivity with a novel approach to progressive rendering of digital images. We also suggest several opportunities for its application to other areas of image processing and computing.

Date of creation, presentation, or exhibit



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

Copyright 1996 Springer.

The greatest level of thanks go to my many students who have participated in the development of these ideas in seminars on computer graphics and neural networks, and especially those who have delved deeply into the techniques in their Projects and Theses (see the bibliography).

Thanks are also due to my colleagues at Kodak Health Imaging Systems, Inc., and the Rochester Institute of Technology who provided invaluable feedback - especially Staszek Radziszowski and Frank Bernhart who reviewed an early draft of this paper for me. And many thanks to the anonymous referee from the Fibonacci Association who provided excellent constructive feedback.

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)


RIT – Main Campus