An applet that draws one-dimensional Brownian motion.
Click the mouse in the window to start zooming.
Click again to stop.
Since Brownian motion is self-similar in law, all of the
zoomed pictures look the same. Contrast with the
The vertical axis is continuously rescaled so that the portion
of the process visible in the window fills the window. This
is arguably wrong, because it makes the zooming look funny,
but also arguably right, because it works for general,
non-self-similar stochastic processes like the
Eventually the discreteness of computer floating-point arithmetic
wrecks the simulation. We can't display the process on a grid
smaller than the smallest representable positive number.
For some statistical Java applets by other people, see
Back to my home page.