move 2 mm (200% of its size) than it would be to see a 100-m object move the same distance (0. 002% of its size). 4. GENERAL DISCUSSION The fractal space described here was chosen not only forits multiscale elegance but for its potential applicabilityto real-world images and image sequences. Fractals—mathematical entities that are self-similar over manyspatial or temporal scales—are ideal tools for represent-ing natural phenomena that take place on many scalesand for studying vision, which contains multiple channelstuned on the spatial and temporal dimensions. Randomfractal textures (sometimes called fractional Browniantextures) have been widely studied because their 1/ f b spectra simulate the spectra of natural images without being confounded by phase information. If bis in the range of a typical natural object ( b50. 9-1. 2),11subjects will often spontaneously report its appearance12: a psy-chophysical version of the venerable children's game ofnaming the shapes in clouds. If phase is manipulated,fractal textures can take on the appearance of naturalscenes: Fractal forgeries of landscapes, coastlines andclouds are extremely compelling. 13,14In the temporal di-mension, sequences of events with 1/ faspectra are ubiq-uitous and fractal forgeries are especially striking; 1/ f acoustic sequences sound musical. 36In vision, 1/ faam-plitude spectra are found for dynamic images, where ais indicative of the character of the movement. 18,28-31The use of a common mathematical framework for character-izing both dynamic noise and dynamic images may alsofacilitate the study of masking of images by noise. ACKNOWLEDGMENTS We thank Jer Sen Chen, Steven Fullenkamp, and Eric Heft for technical support. Douglas Cunningham's current address is Max Planck Institute for Biological Cybernetics, Spemannstrasse 38,Tubingen 72076, Germany. REFERENCES AND NOTES 1. D. B. Judd and G. Wyszecki, Color in Business, Science and Industry, 2nd ed. (Wiley, New York, 1963). 2. G. 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The case closest to our stimuli that hasbeen studied in statistical physics is Brownian motion on afractal fractured surface. The temporal frequency spec-trum exponent afor this case is 0. 5. W. Lehr, J. Machta,2412 J. Opt. Soc. Am. A/Vol. 18, No. 10/October 2001 Billock et al.