Dynamics of screening in multifractal growth

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Abstract
This paper presents a theoretical discussion of fractal growth. The distribution of growth probabilities on the evolving surface of many self-similar systems can be interpreted by a scaling or multifractal formalism. The extremities of the fractal contain the newest material from which further growth is likely to occur. A spatially fixed point in this peripheral region will quickly become screened, or shielded by the addition of new material nearby. The probability of growth from a chosen site will therefore decrease. We give a quantitative description of this process. We introduce the concept of length-scale-dependent exponents and predict that the active zone of the structure is determined by the q=1/2 moment of the probability measure. We also discuss the behavior of the most screened portions of the fractal, and the idea of time correlations in the growth.