The review that @Anyon cited focuses on the use of fractal geometry to classify and model the structure of disordered materials, e.g. structures synthesized by the sol-gel method.
The computational work is nicely summarized in the following figure taken from the paper:

Here "Reaction-Limited", "Ballistic" and "Diffusion-Limited" correspond to 3 different types of simulations, and each model specifies different growth kinetics. In these simulations, particles are moving in random walks and growth occurs when certain conditions are met.
"Monomer-Cluster" simulations start with a seed at a particular site and the growth events happen when a monomer lands on a site neighboring the seed, increasing the seed size. On the other hand, in "Cluster-Cluster" simulations, the seeds are allowed to move around and interact with each other, resulting in extended structures.
The D values on the bottom-left corner of each simulation correspond to the fractal dimension. In a 3D embedding space, this dimension relates the mass ($M$) of an object to its size ($R$)
\begin{equation}
M \sim R^{D}.
\end{equation}
In a 2D embedding space, the surface area ($S$) and size of an object are related through the surface fractal dimension ($D_S$)
\begin{equation}
S \sim R^{D_S}.
\end{equation}
Moreover, when scattering techniques are used on fractal objects, the intensity ($I$) of the incidental beam is related to the wave vector ($K$), through:
\begin{equation}
I \sim K^{-2D+D_S}.
\end{equation}
These relationships, along with the simulations mentioned previously, allow to classify structures and identify the growth factors in kinetic growth systems.