Abstract
A competing two-species growth model, which is a generalized directed percolation, is presented to study the fractal structure of a self-affine pattern at the phase transition point. The growth model is described in terms of a stochastic cellular automaton. The morphology and the phase transition are investigated by using computer simulation. The phase diagram and the composition ratio in the steady state are found. The fractal structures of self-affine patterns along the phase transition line are investigated. Its fractal dimension d f =1.48±0.02 is found on the transition line. Also, near a singular point, the crossover from the Sierpinski gasket to the homogeneous mixture is found. A mean-field theory is presented.
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