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  • Letter

Dimension of diffusion-limited aggregates grown on a line

Eviatar B. Procaccia1,4 and Itamar Procaccia2,3

  • 1Faculty of Industrial Engineering and Management, The Technion, Haifa 32000, Israel
  • 2Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel
  • 3Center for Optical Imagery Analysis and Learning, Northwestern Polytechnical University, Xi'an 710072, China
  • 4Department of Mathematics, Texas A&M University, College Station, Texas 77840, USA

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Phys. Rev. E 103, L020101 – Published 9 February, 2021

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

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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Phys. Rev. E 103, L020101– Published 9 February, 2021
  • Received 12 October 2020
  • Accepted 25 January 2021
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