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Fractal Growth from Local Instabilities

Raffaele Cafiero·Guido Caldarelli
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Abstract

We study, both with numerical simulations and theoretical methods, a cellular automata model for continuum equations describing growth processes in the presence of an external flux of particles. As a result of local instabilities we find a fractal regime of growth for small external fluxes. The growing tip is selected with probability proportional to the curvature in the point. A parameter $p$ gives the probability of lateral growth on the tip. The value of $p$ determines the fractal dimension of the aggregate. Furthermore, for each value of $p$ a cross-over between two different fractal dimensions is observed. Instead, the roughness exponent $χ$ of the aggregates does not depend on $p$ ($χ\simeq 0.5$). Fixed scale transformation approach is applied to compute theoretically the fractal dimension for one of the branches of the structure.

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Raffaele Cafiero, Guido Caldarelli. 2000-10-11. Fractal Growth from Local Instabilities. https://doi.org/10.1209/epl%2Fi2001-00294-2

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