Papers › Bias-free simulation of diffusion-limited aggregation on a square lattice
Bias-free simulation of diffusion-limited aggregation on a square lattice
Yen Lee Loh
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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 10⁸ particles on 65536×65536 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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