Screening in multifractal growth

For any multifractal growth process we calculate how the probability of advance of a fixed site on the boundary of the structure changes as the fractal increases in size. We are then able to find expressions for the dimension of the active zone of the fractal and the distribution of ages of points from which growth occurs in terms of the scaling function f(α). For the case of diffusion-limited aggregation (DLA) and the screened-growth model, we offer a geometrical interpretation of the results. For DLA in arbitrary space dimensions we find a relation between the third moment of the probability distribution and the Hausdorff dimension D, which generalizes a result by Halsey [Phys. Rev. Lett. 59, 2067 (1987)]