The Singularity Spectrum f(α) of Some Moran Fractals

Abstract.

We show that the multifractal decomposition behaves as expected for a family of sets E known as homogeneous Moran fractals associated with the Fibonacci sequence ω, using probability measures μ(ω) associated with the Fibonacci sequence ω. For each value of a parameter α∈ (α_min, α_max), we define ‘multifractal components’ E_α of E, and show that they are fractals in the sense of Taylor. We give the explicit formula for the dimension of E_α. Also our method can be used for the Moran fractals associated with some more general sequences.