Fractal Growth from Local Instabilities

Details Fractal Growth from Local Instabilities Fractal Growth from Local Instabilities

2000-09-15

arxiv.org/abs/cond-mat/0009231v2

Physics

Condensed Matter

Statistical Mechanics

7 pages, 5 figures, submitted to EPL

Scientific paper

10.1209/epl/i2001-00294-2

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 $\chi$ of the aggregates does not depend on $p$ ($\chi \simeq 0.5$). Fixed scale transformation approach is applied to compute theoretically the fractal dimension for one of the branches of the structure.

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