Fractal Analysis of Perceptual Categorization

Fractal geometry has yielded novel investigations, and ultimately a fresh way of understanding the world. Since Euclid formulated the principles of geometry, simple geometric forms have modeled real-world forms. However, the world is not constructed of perfect forms; rather, much of the world is composed of irregular shapes with nonlinear properties. Given the complexity of human psychology, some have begun to relate fractal geometry in psychological models, even claiming the brain to be a fractal pattern-producing machine. This study replicated previous investigations on a well-established phenomenon in psychophysics, namely reaction time differences when judging variation in separable and integral stimuli. When stimulus dimensions are integral, such as height and width of rectangles, subjects are less able to attend to the dimensions independently. Therefore, correlated variation of the dimensions speeds reaction times; whereas, orthogonal variation slows reaction times. With separable stimuli these differences are not observed because presumably individuals are able to attend to the dimensions independently. In addition to analyzing reaction times, as is typical, the current study also analyzed the pattern of response times through lognormal frequency distribution functions in order to test predictions of possible fractal properties of response times. With the integral stimuli, as the categorization task increased in difficulty the more variability was evident in the distributions. Specifically, the distribution became stretched toward the slow-tail of the distribution in a pattern consistent with the research hypothesis. These differences were not seen with separable stimuli. Findings indicate that concepts from fractal geometry may be an appropriate and instrumental way of understanding perceptual categorization