The Fractal Nature of Geographic Phenomena

Abstract

Fractal concepts have attracted substantial popular attention in the past few years. The key ideas originated in studies of map data, and many of the applications continue to be concerned with spatial phenomena. We review the relevance of fractals to geography under three headings; the response of measure to scale, self-similarity, and the recursive subdivision of space. A fractional dimension provides a means of characterizing the effects of cartographic generalization and of predicting the behavior of estimates derived from data that are subject to spatial sampling. The self-similarity property of fractal surfaces makes them useful as initial or null hypothesis landscapes in the study of geomorphic processes. A wide variety of spatial phenomena have been shown to be statistically self-similar over many scales, suggesting the importance of scale-independence as a geographic norm. In the third area, recursive subdivision is shown to lead to novel and efficient ways of representing spatial data in digital form and to be a property of familiar models of spatial organization. We conclude that fractals should be regarded as a significant change in conventional ways of thinking about spatial forms and as providing new and important norms and standards of spatial phenomena rather than empirically verifiable models.

Key Words:

• fractals
• fractional dimension
• self-similarity
• scale
• spatial sampling
• topography
• simulation
• spatial data structure
• recursive subdivision