Brownian Motion is a "stochastic process" used to model many real-world phenomena, including motion of particles. A stochastic process is a process that (motion, e.g.) that changes with random behavior.
To get more technical, something moving under Brownian motion will have movement that does not depend in any way on the past or future. Furthermore, its displacement over time is distributed normally with mean 0 and variance equal to the amount of time. This process lies at the heart of stochastic analysis.
I created Mac Brownian Motion so that I could visualize such a process. This program has no frills, few features, and a narrow purpose. I hope its purpose (to visualize the "path" a particle takes under Brownian motion over time) suits your needs. It's completely free.
To use this program:
Select an x maximum, y maximum, and y minimum (x minimum is always zero). Select the number of points (more points gives a better visualization, but takes longer). Finally, select the color you want the path to take. Then hit "simulate" and watch. You can also save this to a pict file.
Notes: you can show more than one realization on a graph if you don't clear or resize between simulations. That's the reason for the colors.
Also, closing the window quits. If there's demand, I'll allow multiple windows, but this seemed to be the easiest way at this point.
Usage, source code, licensing, and other stuff
I feel that there is a shortage of scientific software for the Mac at this point. SAS Institute, Inc., MathWorks, and others have dropped support and development for their software for data analysis and visualization. There is an opportunity for shareware developers to fill in the gap. Therefore, if you want to work on development of this program, feel free to. If you email me (see below), I can email you the source code, written with REALbasic. You can feel free to modify and redistribute the program free of charge (as long as you keep this document with it and don’t take credit for what is not yours). If you want to write a shareware program, we can negotiate.
