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Multifractal decomposition of fractals with finite memory. (English) Zbl 1150.60004
Summary: The authors study recursive structures with “finite memory” in the Euclidean metric space and the multifractal decomposition of the corresponding fractals. For any two positive numbers \(q, \beta\), and such a recursive structure, a linear operator \(V^{q, \beta}\) in finite dimensional space is defined. The multifractal spectrum is given by the spectral radius of \(V^{q, \beta}\).
MSC:
60D05 Geometric probability and stochastic geometry
28A80 Fractals
60G18 Self-similar stochastic processes
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