Fractal geometry ©

Fractal geometry is an alternative, but complimentary geometry to traditional Euclidean geometry. It is a relatively new type of geometry and has not been clearly defined.

Fractals are self-similar objects that cannot be described in common Euclidean fashion, and are non-uniform in space. Self-similarity means that as magnification (the scale) changes, the shape (the geometry) of the fractal does not change. Fractals have infinite detail, infinite length and a fractal dimension.

Coastlines are perfect examples of fractal geometry. If the coast line is viewed from an aircraft it looks like a crinkled edge, the length of which could be measured. However if you walked along the coast you would notice that each of the crinkles also has crinkled edges and if you measured to length of all these edges you would arrive at a much larger length. Pulling out a magnifying glass would show further self-similar crinkles and even more length, and so on ad-infinitum.

Fractal geometry has been used in forestry in a descriptive way:

Leaf shape
Tree branching patterns
Tree crown arrangements
Tree models
Spatial arrangement of vegetation patches

Other potential areas include:

Species diversity
Animal movement patterns
Forest disturbance
Data storage and compression

For further information:

Lorimer, N.D., R.G. Haight and R.A. Leary (1994) The Fractal Forest: Fractal geometry and applications in forest science. USDA Forest Service General Technical Report NC-170. 43pp.
Mandlebrot B.B. (1982) The fractal geometry of nature. W.H. Freeman & Co. New York.

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Document URL	http://online.anu.edu.au/Forestry/mensuration/FRACTAL1.HTM
Editor	Cris Brack ©
Last Modified Date	Fri, 9 Feb 1996