The perception of natural contour.

The observation that natural curves and surfaces are often fractal suggests that people may be sensitive to their statistical properties. The perceptual protocols that underlie discrimination between fractals and between other types of random contour and fractals are examined. Discrimination algorithms that have precisely the same sensitivities as human observers are constructed. These algorithms do not recognize the integrated scale hierarchy intrinsic to fractal form and operate by imposing a metatheory of structure that is based on a signal-noise distinction. The success of the algorithms implies that (a) self-affinity in random fractals is not perceptually recovered and (b) people have a natural disposition to view contour in terms of signal and noise. The authors propose that this disposition be understood as a principle of perceptual organization. The environment that we live in has essentially two architectural components: One is carpentered, designed, and built by people; the other is everything else, the material form of nature. If one observes carpentered structures with an unjaded eye, it is difficult not to be struck by the smoothness of the surfaces and the cleanness with which the lines are cut. Even the crudest and least adorned structures have these properties. The things that people make are at least minimally designed, and the primitives of design are lines and planes. This is as true of primitive structures and implements as it is of the things that are built today. An inspection of natural structures reveals an entirely different order. The boundaries that form natural surfaces and contours are often not smooth. Natural form—landscapes, mountain ranges, coastlines, stream paths, clouds, tree lines, vegetation cover—is irregular and rough in appearance. The apparent transparency of this observation belies the subtlety that is required to fully appreciate its import. Geometric descriptions of natural structures required the development of a new set of elements that differ radically from those that comprise Euclidean geometry as well as new modes of analysis that depart from the smoothness assumptions on which differential geometry rests. Real analysis, as developed by Cauchy, Weierstrass, and Bolzano, treats structures that have specific properties under mag