Dimensions of fractals in the large

M.R. Allen, G.S.H. Cruttwell, Kathryn E. Hare and J.-O. Rönning

Chaos, Solitons & Fractals, 2007, vol. 31, issue 1, 5-13

Abstract: Fractals in the large can be generated as the invariant set of an expansive, iterated function system. A number of dimensions have been introduced and studied for such fractals. In this note we show that these dimensions coincide for large fractals generated by functions with arithmetic expansion factors, and that this common dimension is equal to the dimension of the (small) fractal generated by the inverse functions.

Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:31:y:2007:i:1:p:5-13

DOI: 10.1016/j.chaos.2005.09.045

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