The Study Of Fractal Growth In Disorder System

Firstly, We generalize the development of fractal theory, the definition of fractals and fractional dimension, and the physical mechanism of the fractal occurrence. Then, the Diffusion Limited Aggregation (DLA), Dielectric Breakdown (DBM), Viscous Fingering and Percolation models are introduced simply.And then, We construct two different kinds of Sierpinski carpets by means of the Mapping Dilation Method in the artical, and apply Monte Carlo method to study Diffusion Limited Aggregation(DLA)growth in two different kinds of Sierpinski carpets. Based on the different setting seed, pattern structures about DLA growth in two different kinds of Sierpinski carpets are obtained by computer simulation, count their fractal dimension, obtain their multifractal spectrum.By means of hole-position randomizing method, to build the random Sierpinski carpet, apply Monte Carlo method to study Diffusion Limited Aggregation(DLA)growth in random Sierpinski carpets, and obtain the pattern structure.We introduced to the formation process of percolation cluster briefly. We afford to pattern structures about DLA growth in different occupied probability P in percolation cluster, count their fractal dimension, and obtain the fractal dimension increase with the occupied probability P increase.Finally, we obtain the Laplace equation of anisotropy diffusion DLA cluster. in DLA cluster with linseed, we receive the pattern structure, count their fractal dimension, obtain their multifractal spectrum.