Fractal and Multifractal Properties of Poissonian Growth

A growth model governed by the Poisson equation is presented to simulate the aggregation process in sputter (or vapor)-deposited thin films. By using computer simulation, it is found that the fractal dimension of the aggregates is consistent with that of diffusion-limited aggregation (DLA) at an initial stage and increases with time. The multifractal structure of the growth probability distribution is derived by making use of the Monte Carlo estimation. It is shown that the Poissonian growth pattern has characteristic fractal and multifractal properties.