Hier is another model by Mike Borrello: This VisSim diagram demonstrates random walk in three dimensions and illustrates the exemplar behavior of a small drop of red dye released into a container of water and the diffusion process that ensues.

To fully visualize full perspective of the trajectory, press and hold the ctrl key, place the cursor at one corner of the plot and drag it with the mouse to rotate. For more information on the mathematics, see the Wikipedia article on Brownian motion.

Here are three models showing the Barnsley fern with two variations (constants changed).