NUMB3RS - Season 2 - "Rampage" - I...It...Itera...Iteration

Brownian motion can be modeled in two dimensions using a sequence of random steps. Let's start at the origin $(0,0)$. At each step $n$, we generate a random vertical change ($\Delta y$) and a random horizontal change ($\Delta x$) using a standard normal distribution where the mean is $\mu = 0$ and the standard deviation is $\sigma = 1$.

The formulas to update our coordinates are: $x_{n+1} = x_n + \Delta x$ $y_{n+1} = y_n + \Delta y$

Because the mean step size is $0$, the path has equal probability of going in any direction, resulting in an unpredictable, wandering path called a random walk.