# From fractals in external DLA to internal DLA on fractals

## TL;DR

This paper compares external and internal DLA growth models on graphs, highlighting their contrasting behaviors and exploring their dynamics on fractal structures like Sierpinski gaskets and carpets.

## Contribution

It introduces a unified framework for analyzing external and internal DLA models on infinite and fractal graphs, revealing their distinct growth patterns.

## Key findings

- External DLA forms fractal, irregular structures.
- Internal DLA produces regular, filled clusters.
- Results on DLA behavior on Sierpinski fractals.

## Abstract

We present an unified approach on the behavior of two random growth models (external DLA and internal DLA) on infinite graphs, the second one being an internal counterpart of the first one. Even though the two models look pretty similar, their behavior is completely different: while external DLA tends to build irregularities and fractal-like structures, internal DLA tends to fill up gaps and to produce regular clusters. We will also consider the aforementioned models on fractal graphs like Sierpinski gasket and carpet, and present some recent results and possible questions to investigate.