Multifractal decomposition of Moran Fractals

Abstract We analyze the multifractal decomposition of Moran fractals using Olsen Multifractal Measure (OMM). show that this measure is non-singular when Halsey’s partition function takes value 1, result has two consequences, one them defines mass τ ( q ), other it also a statistical ν in terms probability vector P ). The Hausdorff dimension f ) concentration set equal with Holder exponent evaluated , equality implies = α – Finally, results Cawley and Mauldin shown D Dim H J Legendre Transform where J α = { x ∈ M ∣ lim r → 0 ln ⁡ μ stretchy="false">( B , stretchy="false">) } i.e. qα