The Singularity Spectrum f(α) of Some Moran Fractals

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∈ (αmin, αmax), we define ‘multifractal components’ Eα of E, and show that they are fractals in the sense of Taylor. We give the explicit formula for the dimension of Eα. Also our method can be used for the Moran fractals associated with some more general sequences.