Dimensions of random affine code tree fractals

TL;DR

This paper determines the Hausdorff dimension of a broad class of random affine planar code tree fractals, including measures from random V-variable and Markov models, advancing understanding of their geometric complexity.

Contribution

It introduces a general framework for calculating the Hausdorff dimension of random affine code tree fractals, encompassing various natural probabilistic models.

Findings

Almost sure Hausdorff dimension computed for the class of fractals.

Includes measures from random V-variable and homogeneous Markov processes.

Provides a unified approach to fractal dimension in random affine constructions.

Abstract

We calculate the almost sure Hausdorff dimension for a general class of random affine planar code tree fractals. The set of probability measures describing the randomness includes natural measures in random $V$-variable and homogeneous Markov constructions.