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Research Report MRR95-019
Deterministic And Random Fractals
John Hutchinson
Abstract:
This is a preprint of a chapter in Complex Systems, edited by T.
Bossomaier and
D. Green and to be published by Cambridge University Press. The material is
expository and the mathematical level is elementary. I have even attempted to
motivate and develop from first principles the relevant notions of metric
spaces,
measure theory and probability theory.
The scaling law approach to deterministic and random fractals is outlined.
For each scaling law there is exactly one associated fractal which is invariant
under that law. An initial seed will converge under successive
iterations of
the scaling operator to this fractal. Fractal approximations,
fractal
coding, parameter space, and dimension are discussed.
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