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We introduce a new universality class of one-dimensional iteration modelgiving rise to self-similar motion, in which the Feigenbaum constants aregeneralized as self-similar rates and can be predetermined. The curves of themean-square displacement versus time generated here show that the motion is akind of anomalous diffusion with the diffusion coefficient depending on theself-similar rates. In addition, it is found that the distribution ofdisplacement agrees to a reliable precision with the q-Gaussian typedistribution in some cases and bimodal distribution in some other cases. Theresults obtained show that the self-similar motion may be used to describe theanomalous diffusion and nonextensive statistical distributions.

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