Brownian motion
is one of the most familiar examples of a random fractal process. Here we show
how to use the random fractal cartoon method to simulate Brownian motion.
First, we select the initiator and generator, and
show how this choice is related to Brownian motion.
Second, we iterate the construction,
obtaining a cartoon with the right scaling, but far too regular to be a forgery
of natural Brownian motion.
Finally, we randomize the construction,
obtaining good forgeries.