Fig. 5: Interpolate Sierpiński gasket.
a Mean square distance MSD(t) of a particle in an interpolating lattice, cf. Fig. 1c, characterized by the ratio \(\gamma \equiv {J}^{{\prime} }/J\) between hopping parameters \({J}^{{\prime} }\) exclusive to the regular lattice, and J in both regular and fractal lattice. We initialize the evolution in one corner of an interpolating gasket of generation 7. The slowest behavior is obtained in a fully fractal geometry (γ = 0), whereas the fastest behavior corresponds to regular triangular lattice (γ = 1). b For the different values of γ, we extract the exponent α of the mean square distance (from fits to the curves in (a) in the intermediate regime marked by the dashed lines). The result is plotted as a function of γ. The error bars of the fitted α are smaller than the circles displayed. a is the distance between neighbor sites.
