ABSTRACT
Simulation of unbiased one-dimensional random walks lead to surprising results: the mean displacement is zero and the random walk variance increases proportional to the step number. This chapter builds further connections between random walks, Brownian motion, and the partial differential equation for diffusion. Brownian motion is studied using the workflow Do Once → Do several times → Summarize → Visualize. The associated statistics (mean and variance) from this workflow are consistent with predictions from a normally distributed random variable whose variance grows in time.
