The Brownian motion (or Wiener process) is a fundamental object in mathematics, physics, and many other scientific and engineering disciplines. This model describes the movement of a particle suspended in a fluid resulting from random collisions with the quick molecules in the fluid (diffusion). More generally, the Brownian motion models a continuous-time random walk, where a particle evolves in space by making independent random steps in all directions.

Mathematically, the Brownian motion is a particular Markov continuous stochastic process. The Brownian motion is at the core of mathematical domains such as stochastic calculus and the theory of stochastic processes, but it is also central in applied fields such as quantitative finance, ecology, and neuroscience.

In this recipe, we will show how to simulate and plot a Brownian motion in two dimensions.