Diffusion-limited aggregation as a Markovian process: Bond-sticking conditions

Cylindrical lattice diffusion limited aggregation (DLA), with a narrow widt h N, is solved using a Markovian matrix method. This matrix contains the pr obabilities that the front moves from one configuration to another at each growth step, calculated exactly by solving the Laplace equation and using t he proper normalization. The method is applied for a series of approximatio ns, which include only a finite number of rows near the front. The matrix i s then used to find the weights of the steady-state growing configurations and the rate of approaching this steady-state stage. The former are then us ed to find the average upward growth probability, the average steady-state density and the fractal dimensionality of the aggregate, which is extrapola ted to a value near 1.64.