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Anomalous diffusion processes, in particular superdiffusive ones, are knownto be efficient strategies for searching and navigation by animals and also inhuman mobility. One way to create such regimes are L\'evy flights, where thewalkers are allowed to perform jumps, the "flights", that can eventually bevery long as their length distribution is asymptotically power-law distributed.In our work, we present a model in which walkers are allowed to perform, on a1D lattice, "cascades" of $n$ unitary steps instead of one jump of a randomlygenerated length, as in the L\'evy case, where $n$ is drawn from a cascadedistribution $p_n$. We show that this local mechanism may give rise tosuperdiffusion or normal diffusion when $p_n$ is distributed as a power law. Wealso introduce waiting times that are power-law distributed as well andtherefore the probability distribution scaling is steered by the two PDF'spower-law exponents. As a perspective, our approach may engender a possiblegeneralization of anomalous diffusion in context where distances are difficultto define, as in the case of complex networks, and also provide an interestingmodel for diffusion in temporal networks.

Onset of anomalous diffusion from local motion rules