Line models for snowflake crystals and their Hausdorff dimension
type: Item
instance of: scholarly article
zbMATH Open document ID: 1002.60099
author: Jonathan Croft
publication date: 2003-01-01T00:00:00Z
Mathematics Subject Classification ID: 60K40
Mathematics Subject Classification ID: 82C24
Mathematics Subject Classification ID: 82D25
Mathematics Subject Classification ID: 28A80
zbMATH DE Number: 1701850
zbMATH Keywords: Hausdorff dimension
zbMATH Keywords: fractal
zbMATH Keywords: snowflake crystal
zbMATH Keywords: diffusion limited aggregation
MaRDI profile type: Publication
title: Line models for snowflake crystals and their Hausdorff dimension
review text: The author describes a family of stochastic recursive line models with possible branching that can be used to model fractal objects like snowflakes. In difference to diffusion limited aggregation (DLA) models of snowflakes-like objects, these new models are better tractable mathematically and can be physically motivated. These line models are defined on triangular lattice and provide examples of random von Koch curves. The author shows that under a simple condition (called the R-condition), the Hausdorff dimension exists almost surely and admits an explicit description. When the R-condition is broken, the dimension is shown to exist almost surely via Oseledets' theorem on random matrix products.NEWLINENEWLINEFor the entire collection see [Zbl 0968.00043].
reviewed by: Ilya S. Molchanov
description: scientific article; zbMATH DE number 1701850