Multifractal Decomposition of Fractals With Finite Memory

The authors study recursive structures with “finite memory” in Euclidean matric space and the multifractal decomposition of the corresponding fractals. For any two positive numbers q, β, and such a recursive structure, a linear operator Vq, β in finite dimensional space is defined. The multifractal spectrum is given by the spectral radius of Vq, β.