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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.  [Fractal Dimension] In ordinary geometry, the volume of an object scales up in the power of the dimension of the space in which the object resides.  \[ V = k r^D\]  for example, by making the side of a square twice as long we quadruple its volume. By making the side of a cube twice as long we multiply the volume by 8. The same notion could be used the define the dimensionality of a fractal, interestingly, the   dimensionality of fractal differs from the space it resides in.  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 sticks to it and becomes "sticky" too. Further walkers the reaches it stick as well, creating clusters. The model is simple, but the patterns produced are rich and "organic" looking. 
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