LETTER: Self-similar motion for modeling anomalous diffusion and nonextensive statistical distributions

We introduce a new universality class of one-dimensional iteration models giving rise to self-similar motion. The curves of the mean square displacement versus time show that the motion is a kind of anomalous diffusion with the diffusion coefficient depending on the self-similar rates. Moreover, it is found that the distribution of the displacement agrees to a reliable precision with the q-Gaussian type distribution in some cases and the bimodal distribution in some other cases. The results show that the self-similar motion may be used to investigate anomalous diffusion and nonextensive statistical distributions.