Bias-free simulation of diffusion-limited aggregation on a square lattice

Yen Lee Loh

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arXiv · 1407.2586

Bias-free simulation of diffusion-limited aggregation on a square lattice

Yen Lee Loh

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Abstract

We identify sources of systematic error in traditional simulations of the Witten-Sander model of diffusion-limited aggregation (DLA) on a square lattice. We present an algorithm that reduces these biases to below $10^{-12}$. We grow clusters of $10^8$ particles on $65536\times 65536$ lattices. We verify that lattice DLA clusters inevitably grow into anisotropic shapes, dictated by the anisotropy of the aggregation process. We verify that the fractal dimension evolves from the continuum DLA value, $D=1.71$, for small disk-shaped clusters, towards Kesten's bound of $D=3/2$ for highly anisotropic clusters with long protruding arms.

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Yen Lee Loh. 2014-07-09. Bias-free simulation of diffusion-limited aggregation on a square lattice. https://arxiv.org/abs/1407.2586

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