Line models for snowflake crystals and their Hausdorff dimension (Q2769669)

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].