The Fractal Nature of Geographic Phenomena

Michael F. Goodchild, David M. Mark

Research output: Contribution to journalReview articlepeer-review

270 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)265-278
Number of pages14
JournalAnnals of the Association of American Geographers
Issue number2
StatePublished - Jun 1987
Externally publishedYes


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

ASJC Scopus subject areas

  • Geography, Planning and Development
  • Earth-Surface Processes


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