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The role of the geometric fluctuations on the multifractal properties of thelocal magnetization of aperiodic ferromagnetic Ising models on hierachicallattices is investigated. The geometric fluctuations are introduced bygeneralized Fibonacci sequences. The local magnetization is evaluated via anexact recurrent procedure encompassing a real space renormalization groupdecimation. The symmetries of the local magnetization patterns induced by theaperiodic couplings is found to be strongly (weakly) different, with respect tothe ones of the corresponding homogeneous systems, when the geometricfluctuations are relevant (irrelevant) to change the critical properties of thesystem. At the criticality, the measure defined by the local magnetization isfound to exhibit a non-trivial F(alpha) spectra being shifted to higher valuesof alpha when relevant geometric fluctuations are considered. The criticalexponents are found to be related with some special points of the F(alpha)function and agree with previous results obtained by the quite distincttransfer matrix approach.Comment: 10 pages, 7 figures, 3 Tables, 17 reference

Multifractal properties of aperiodic Ising model on hierarchical lattices: role of the geometric fluctuations