Dimension of diffusion-limited aggregates grown on a line

Eviatar B. Procaccia; Itamar Procaccia

doi:https://doi.org/10.1103/PhysRevE.103.L020101

Dimension of diffusion-limited aggregates grown on a line

Eviatar B. Procaccia, Itamar Procaccia

Technion - Israel Institute of Technology, Weizmann Institute of Science

Research output: Contribution to journal › Article › peer-review

Abstract

Diffusion-limited aggregation (DLA) has served for 40 years as a paradigmatic example for the creation of fractal growth patterns. In spite of thousands of references, no exact result for the fractal dimension D of DLA is known. In this Letter we announce an exact result for off-lattice DLA grown on a line embedded in the plane D=3/2. The result relies on representing DLA with iterated conformal maps, allowing one to prove self-affinity, a proper scaling limit, and a well-defined fractal dimension. Mathematical proofs of the main results are available in N. Berger, E. B. Procaccia, and A. Turner, Growth of stationary Hastings-Levitov, arXiv:2008.05792.

Original language	English
Article number	L020101
Number of pages	4
Journal	Physical Review E
Volume	103
Issue number	2
DOIs	https://doi.org/10.1103/PhysRevE.103.L020101
State	Published - Feb 2021

All Science Journal Classification (ASJC) codes

Condensed Matter Physics
Statistical and Nonlinear Physics
Statistics and Probability

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https://arxiv.org/abs/2010.05709License: Other

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abstract = "Diffusion-limited aggregation (DLA) has served for 40 years as a paradigmatic example for the creation of fractal growth patterns. In spite of thousands of references, no exact result for the fractal dimension D of DLA is known. In this Letter we announce an exact result for off-lattice DLA grown on a line embedded in the plane D=3/2. The result relies on representing DLA with iterated conformal maps, allowing one to prove self-affinity, a proper scaling limit, and a well-defined fractal dimension. Mathematical proofs of the main results are available in N. Berger, E. B. Procaccia, and A. Turner, Growth of stationary Hastings-Levitov, arXiv:2008.05792.",

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AB - Diffusion-limited aggregation (DLA) has served for 40 years as a paradigmatic example for the creation of fractal growth patterns. In spite of thousands of references, no exact result for the fractal dimension D of DLA is known. In this Letter we announce an exact result for off-lattice DLA grown on a line embedded in the plane D=3/2. The result relies on representing DLA with iterated conformal maps, allowing one to prove self-affinity, a proper scaling limit, and a well-defined fractal dimension. Mathematical proofs of the main results are available in N. Berger, E. B. Procaccia, and A. Turner, Growth of stationary Hastings-Levitov, arXiv:2008.05792.

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Dimension of diffusion-limited aggregates grown on a line

Abstract

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