Hostname: page-component-6bf8c574d5-qdpjg Total loading time: 0 Render date: 2025-02-20T10:38:09.106Z Has data issue: false hasContentIssue false
  • English
  • Français

Fractal Computer Graphics as a Stimulus for the Enhancement of Perceptual Sensitivity to the Natural Environment

Published online by Cambridge University Press:  23 June 2015

John Geake
John Geake*
Affiliation:
Faculty of Education, Work and Training, University of New England, Northern Rivers N.S.W.
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The beauty and freshness of fractal geometry suggests that once again we are at the start of science and mathematics… women and men will look back on this era much as we look back to the early Greeks. (Barnsley, 1989, p. 5)

Such enthusiasm for a perceived new paradigm in the mathematical sciences is beginning to emerge within broader educational contexts (Devaney & Keen, 1989; Egnatoff, 1989; Geake, 1990a & 1990b). Much of the interest in fractal geometry has focussed on its ability to describe complex natural phenomena (Mandelbrot, 1983 & 1990; Pickover, 1987; Barnsley, 1988). Recent investigations into the visual perception of natural imagery have used fractal mathematics in describing the characteristics of such perception (Pentland, 1984; Field, 1987; Peli, 1990). This study examined human visual perception of the fractal form found in the natural environment. Specifically, this research project examined how exposure to a program of fractal computer graphics affected the perceptual sensitivity of primary school children to the natural visual environment. The underpinning rationale was to address a long standing challenge of Linke (1980) to develop a stronger theoretical basis for environmental education in Australia.

Type
Research Article
Information
Australian Journal of Environmental Education , Volume 8 , 1992 , pp. 1 - 16
Copyright
Copyright © Cambridge University Press 1992

References

Barnsley, M. F. Fractals Everywhere: The first course in deterministic fractal geometry, Academic Press, New York, 1988.Google Scholar
Barnsley, M. F. & Sloan, A. D. “A better way to compress images”, Byte, 01, 1988, pp. 215–223.Google Scholar
Barnsley, M. F. The Desktop Fractal Design Handbook, Academic Press, New York, 1989.Google Scholar
Baroni, M. R., Job, R., Peron, E. M. & Salmaso, P. “Memory for natural settings: role of diffuse and focused attention”, Perceptual and Motor Skills, 51, 1980, pp. 883–889.Google Scholar
Berry, M. “Quantum physics on the edge of chaos”, New Scientist, 11, 1987, pp. 44–47.Google Scholar
Brewer, W. F. “Memory for randomly sampled autobiographical events”, in Neisser, U. & Winograd, E. (eds.) Remembering Reconsidered: Ecological and traditional approaches to the study of memory, Cambridge University Press, Cambridge, 1988.Google Scholar
Briggs, J. & Peat, F. D. Turbulent Mirror: an illustrated guide to Chaos Theory and the science of wholeness, Harper & Row, New York, 1989.Google Scholar
Bullock, B. L. “Finding structure in outdoor scenes”, in Chen, C. H. (ed.) Pattern Recognition and Artificial Intelligence, North-Holland, 1976.Google Scholar
Burrough, P. A. “Fractal dimensions of landscapes and other environmental data”, Nature, 294, 1981, pp. 240–242.Google Scholar
Butts, W. L. Children's Science (video), Macquarie University, North Ryde, 1988.Google Scholar
Campbell, V. “Artful chaos from nature's fractals”, The Australian, 12 18, 1990.Google Scholar
Devaney, R. L. & Keen, L. Chaos and Fractals: the mathematics behind the computer graphics, American Mathematical Society Proceedings of Symposia in Applied Mathematics, 39, 1989.Google Scholar
Dewdney, A. K. “Of fractal mountains, graftal plants and other computer graphics at Pixar”, Scientific American, 255(6), 1986, pp. 14–18.Google Scholar
Dewdney, A. K. “Beauty and profundity: the Mandelbrot set and a flock of its cousins called Julia”, Scientific American, 257(5), 1987, pp. 118–122.Google Scholar
Dewdney, A. K. “A tour of the Mandelbrot set aboard the Mandelbus”, Scientific American, 260(2), 1989, pp. 88–91.Google Scholar
Egnatoff, W. J. Fractal Explorations in Secondary Mathematics, Science, and Computer Science, Queen's University, Kingston, Canada, 1989.Google Scholar
Field, D. J. “Relations between the statistics of natural images and the response properties of cortical cells”, Journal of the Optical Society of America, 4(12), 1987, pp. 2379–2394.Google Scholar
Foukal, P. V. “The variable sun”, Scientific American, 262(2), 1990, pp. 26–33.Google Scholar
Gardner, M. “White and brown music, fractal curves and one-over-fluctuations”, Scientific American, 04, 1983, pp. 16–32.Google Scholar
Geake, J. G. “Fractal computer graphics: a window on complex numbers and limits in the real world”, Australian Senior Mathematics Journal, 4(2), 1990a, pp. 86–98.Google Scholar
Geake, J. G. “Chaos in the classroom”, Proceedings of the Australian Mathematics Teachers' Association 13th Annual Conference, Hobart, 1990b, pp. 257–284.Google Scholar
Gleick, J. Chaos: Making a New Science, Viking Penguin, New York, 1987.Google Scholar
Gleick, J. & Porter, E. Nature's Chaos, Scribners, London, 1990.Google Scholar
Haken, H. “Chaos and order in nature”, Springer Series in Synergetics, 11, 1983, 2–11.Google Scholar
Kersten, D. “Predictability and redundancy of natural images”, Journal of the Optical Society of America, 4(12), 1987, pp. 2395–2400.Google Scholar
Knill, D. C., Field, D. & Kersten, D. “Human discrimination of fractal images”, Journal of the Optical Society of America, 7(6), 1990, pp. 1113–1123.Google Scholar
Linke, R. D. “Achievements and aspirations in Australian environmental education”, Journal of Environmental Education, 12(2), 1980, pp. 20–23.Google Scholar
Mandelbrot, B. B. The Fractal Geometry of Nature, W. H. Freeman, New York, 1983.Google Scholar
Mandelbrot, B. B. “Fractals - a geometry of nature”, New Scientist, 09, 1990, pp. 22–27.Google Scholar
Milne, A. K. “Landsat imagery and teaching about the environment”, Geographical Education, 3, 1979, pp. 319–330.Google Scholar
Ottino, J. M. “The mixing of fluids”, Scientific American, 260(1), 1989, pp. 40–49.Google Scholar
Peitgen, H. O. & Richter, P. H. The Beauty of Fractals: Images of Complex Dynamical Systems, Springer-Verlag, Berlin, 1986.Google Scholar
Peitgen, H. O. & Saupe, D. (eds.) The Science of Fractal Images, Springer-Verlag, Berlin, 1988.Google Scholar
Peli, T. “Multiscale fractal theory and object characterization”, Journal of the Optical Society of America, 7(6), 1990, pp. 1101–1112.CrossRefGoogle Scholar
Pentland, A. P. “Fractal-based description of natural scenes”, Transactions on Pattern Analysis and Machine Intelligence, 6(6), 1984, pp. 661–674.Google Scholar
Pickover, C. A. “Blooming Integers”, Computer Graphics World, 03, 1987, pp. 54–57.Google Scholar
Rejeski, D. W. “Children look at nature: environmental perception and education”, Journal of Environmental Education, 13(4), 1982, pp. 27–40.Google Scholar
Schibeci, R. “Self-organisation: astronomical, biological and geological structures:, The Australian Science Teachers Journal, 35(4), 1989, pp. 11–14.Google Scholar
Sia, A. P. Challenge to preservice education: integrating environmental education in the school curricula. 65th Annual Conference of ATE, Las Vegas, 1985.Google Scholar
Smith, D. “Shaping up to the future with fractals”, Sydney Morning Herald, 12 17,1990.Google Scholar
Sorensen, P. “Fractals: exploring the rough edges between dimensions”, Byte, 09, 1984, pp. 157–172.Google Scholar
Treisman, A. “Properties, parts and objects”, in Boff, K. R., Kaufman, L. & Thomas, J. P. (eds.) Handbook of Perception and Human Performance (Vol. II), John Wiley & Sons, New York, 1986.Google Scholar
Watson, A. B., Barlow, H. B. & Robson, J. G. “What does the eye see best?”, Nature, 302, 1983, pp. 419–422.Google Scholar
Winn, W. “Visual information processing: a pragmatic approach to the imagery question”, Educational Communication and Technology Journal, 28, 1980, pp. 120–133.Google Scholar