Multifractal decomposition of fractals with finite memory. (English) Zbl 1150.60004

Yu, Jinghu; Zhang, Xiaoli

Acta Math. Sci., Ser. B, Engl. Ed. 28, No. 1, 151-162 (2008).

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