We study models that use random numbers to generate statistically predictable outcomes. Examples include Monte Carlo methods and random walks on a lattice. Many of the random walk models are described in Chapter 7 of An Introduction to Computer Simulation Methods.
The Diffusion Limited Aggregation (DLA) Model shows the growth of a DLA cluster such as a soot particle.
The following EJS models use random numbers to generate statistically predictable outcomes.
Wikipedia: http://en.wikipedia.org/wiki/Galton_board
The Diffusion Limited Aggregation Model was created by Wolfgang Christian using the Easy Java Simulations (EJS) authoring and modeling tool. You can examine and modify a compiled EJS model if you run the program by double clicking on the model's jar file. Right-click within the running program and select "Open EJS Model" from the pop-up menu to copy the model's XML description into EJS. You must, of course, have EJS installed on your computer.
Information about EJS is available at: <http://www.um.es/fem/Ejs/> and in the OSP comPADRE collection <http://www.compadre.org/OSP/>.