A dimensional consideration is presented to obtain the fractal dimension D of the diffusion-limited aggregates which grow in a space with general dimensionality d s (any number ≧1) through deposition of diffusing particles following trajectories with a fractal dimension d w (Levy flight). We find rigorously D =( d s 2 + d w -1)/( d s + d w -1), which is in excellent agreement with many computer simulation results.
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Honda et al. (1986) studied this question.