The singularity spectrum of some non-regularity moran fractals

In this paper, we shall study the multifractal decomposition behavior for a family of sets E known as Moran fractals. For each value of the parameter α ∈ (αmin, αmax), we define “multifractal components” Eα of E, and show that they are non-regularity fractals (in the sense of Taylor). By obtaining the new sufficient conditions for the valid multifractal formalisms of non-regularity Moran measures, we give explicit formula for the Hausdorff dimension and Packing dimension of Eα respectively. In particular, we describe a large class of non-regularity Moran measure satisfying the explicit formula.

► We discuss the multifractal structures of a particular type of fractals called a non-regularity Moran fractal.
► We show that they are non-regularity fractals (in the sense of Taylor).
► we give explicit multifractal formula.
► we describe a large class of non-regularity Moran measure satisfying the explicit formula.