Dimension Of Diffusion-limited Aggregation Research Articles

Dynamic Tip Front Dimension in Diffusion-limited Aggregation

A new fractal dimension of diffusion-limited aggregation (DLA) is studied by tip front angle near hottest branch projecting bare field, which is obtained from envelope line considering near pentago...

Laplacian growth and diffusion limited aggregation: different universality classes.

It had been conjectured that diffusion limited aggregates and Laplacian growth patterns (with small surface tension) are in the same universality class. Using iterated conformal maps we construct a one-parameter family of fractal growth patterns with a continuously varying fractal dimension. This family can be used to bound the dimension of Laplacian growth patterns from below. The bound value is higher than the dimension of diffusion limited aggregates, showing that the two problems belong to two different universality classes.

Convergent calculation of the asymptotic dimension of diffusion limited aggregates: scaling and renormalization of small clusters

Diffusion limited aggregation (DLA) is a model of fractal growth that had attained a paradigmatic status due to its simplicity and its underlying role for a variety of pattern forming processes. We present a convergent calculation of the fractal dimension D of DLA based on a renormalization scheme for the first Laurent coefficient of the conformal map from the unit circle to the expanding boundary of the fractal cluster. The theory is applicable from very small (2-3 particles) to asymptotically large (n-->infinity) clusters. The computed dimension is D=1.713+/-0.003.