Divine proportion shape preservation and the fractal nature of cluster-cluster aggregates

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Abstract
We present a restricted hierarchial model of cluster-cluster aggregation which allows for an analytical calculation of the fractal dimensions in excellent agreement with those found in Nature and simulations. We argue that this agreement is a consequence of the self-preserving cluster shape common to all models and Nature. This shape determines the fractal dimension and in our model is described by d-dimensional generalizations of the Fibonacci series and the divine proportion.