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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
##### Keywords:
multifractal spectrum; fractal; finite memory; spectral radius
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