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Fractals and Transformations

Authors: Thomas J. Bannon;

Fractals and Transformations

Abstract

In traditional geometry we model nature using the points, lines, and planes of Euclid. Very recently Mandelbrot (1983) gave us fractals to use in building new models. One of the reasons these new fractal models are successful is that a great deal of self similarity is found in nature. Weather patterns over local areas resemble large-scale weather patterns. Branches resemble trees and rocks resemble mountains. The regularities as well as the irregularities of nature repeat at different scales. Geographical features are so self-similar that cartographers must place scales on maps to keep islands from being mistaken for continents or hills for mountains. Self-similarity is a property of many fractals, so whenever nature proves to be self-similar, a fractal will usually furnish a good model of it.

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Powered by OpenAIRE graph
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
Average
Average
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