A sequence of random numbers can be a very simple Monte Carlo simulation. For instance, a list of random numbers generated independently from a normal distribution with mean 0 can simulate a white noise process.
Unlike everwhere in the internet, I've used random numbers using a normal distribution for both x and y coordinates of the particle which are successively sumed with other points to give a path. I tried interpolating among the points but the results were not so impressive as this one. Both 2D and 3D versions available now!
2D version. (This animation is upto 200 frames only)
3D version. (only 300 frames rendered, painstakingly- took quite some time on my computer lol & don't even mention the frequent powercuts here!)
3D version, maybe? :DDone. Check the brownian3d.nb in the sources!
- GNU GPL v3.0 or later on your opinion