Monte Carlo renormalisation group approach to multifractal structure of growth probability distribution in DLA

A Monte Carlo renormalisation group method is presented to study the fractal structure of a DLA cluster. This method converges very rapidly with an increase in the size of the cell. Applying this technique to the DLA grown on the square lattice, the scaling structure of the growth probability distribution in the surface layer is calculated. An infinite set of generalised dimensions D(q) and the alpha -f spectra are found. The author estimates that the maximum value of the generalised dimension and the surface fractal dimension are D infinity =0.5+0.05 and D 0 =1.5+0.05, up to the scale factor b=30, in excellent agreement with the conjecture by Ball (1986).