Anomalous diffusion on random fractal composites

Stochastic fractals, generated from combinations of deterministic fractals, have the advantage of being tractable to some extent, but also being closer to real materials, since they are partially disordered. In the present work, we focus our attention on the remarkable nonlinear mixing behavior exhibited by fractals generated as random combinations of two different Sierpinski carpet generators. When patterns with different anomalous diffusion exponents and the same or different fractal dimensions are combined together, the effective diffusion exponent cannot in general be expressed as a linear weighted average of the diffusion exponents of the constituents. The effective exponent may show a maximum or minimum for certain compositions. An explanation of this interesting phenomenon is offered on the basis of details of the carpet generator, particularly on the number and position of 'connection points', which determine the connectivity of the 'fractal composite'