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\section{Overview}  Diffusion-Limited Aggregation (DLA) is a process whereby particles undergoing Brownian motion aggregate to form clusters of particles, and can be observed in many natural phenomenon, such as the formation of snowflakes and the formation of electrically conducting regions in a dielectric breakdown. These clusters are an example of a fractal, i.e. a pattern that replicates itself in any scale.  The model is simple, but the patterns produced are rich and complex. very "organic" looking.  The primary means to study DLA is by computer simulations, where a random-walker diffuses in the lattice. When it diffuses into a "sticky" site it too becomes "sticky", as well as any other walker that reaches it, creating clusters. In this work, I write a simple MATLAB code to demonstrate some properties of DLA and the patterns that emerge. 
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