# Internal DLA on Sierpinski gasket graphs

## TL;DR

This paper studies the IDLA growth process on Sierpinski gasket graphs, proving that the resulting clusters almost surely fill metric balls, extending understanding of stochastic growth on fractal structures.

## Contribution

It demonstrates that IDLA clusters on Sierpinski gasket graphs almost surely fill metric balls, a novel result for fractal graph structures.

## Key findings

- IDLA clusters fill balls with probability 1
- Extension of IDLA behavior to fractal graphs
- Advances understanding of stochastic growth on fractals

## Abstract

Internal diffusion-limited aggregation (IDLA) is a stochastic growth model on a graph $G$ which describes the formation of a random set of vertices growing from the origin (some fixed vertex) of $G$. Particles start at the origin and perform simple random walks; each particle moves until it lands on a site which was not previously visited by other particles. This random set of occupied sites in $G$ is called the IDLA cluster. In this paper we consider IDLA on Sierpinski gasket graphs, and show that the IDLA cluster fills balls (in the graph metric) with probability 1.