Brownian movement is described as the random movement of particles in liquid. Since the movement is in liquid the motion is in three dimensional. I thought three dimensions might be a bit too much to get started with so I simplified it down to two dimensions. This is a just a quick note to show what I have worked on in the past. It was created in actionscript 2 using bitmap data, the drawing api, and of course the basic fundamentals of brownian movement. I have included some images of the visuals that were created and a link to the tool I created to draw for me.
Use the sliders and text fields to manipulate the results of the visualization tool. Brownian Movement Drawing Tool