# Diffusion Limited Aggregation (DLA) Simulation

Diffusion limited aggregation is simulated in C++ as part of coursework for PH30056 Computational Physics B.

Diffusion limited aggregation (DLA) is a process where particles (walkers) diffuse through space, sticking together when they come into contact, forming a cluster. The cluster formed by DLA processes are fractals, commonly seen in natural growth systems. DLA was first simulated by Witten and Sander who measured the fractal dimension of a small cluster using a computer. Since then major advances in computing technology have allowed for much larger and more complex simulations to be created.

I will explore two different DLA simulations; one provided by A.Souslov and V.Rimpilainen where clusters are grown and visualised in C++ using OpenGL. The fractal dimension is calculated using the radial size of the cluster. The latter simulation is written by myself and predominantly uses box counting to calculate the fractal dimension.

The effect of changing the probability of walkers sticking, and of the density of simultaneously simulated particles will be explored.

An equation is found which gives the density limit for diffusion limited aggregation simulations:

\rho\leq\frac{1}{2\pi\sqrt{\frac{1}{6} N}}

where N is the number of particles in the cluster. This equation is based on the number of particles diffusion per time step being less than the number of particles on the cluster rim.