Brownian Motion

Some early history of Brownian motion.
Brownian motion in the plane, and a first look at scaling.
A clearer picture is the graph of Brownian motion in 1 dimension.
Here are some of the mathematical properties of Brownian motion.
For comparison with data, here are the visual signatures of Brownian motion. Anticipating later work, for amusement we compare these graphs with some stock market data.
Finally, we mention the Brownian bridge, a related construction of some theoretical importance now.

Return to Random Fractals.