In a 1905 issue of Nature, statistician Karl Pearson of University College London asked readers for their help with a problem he named the random walk1: A walker starts at an origin point and walks l yards in a straight line in a random direction. The walker then turns and proceeds another l yards in another random direction, and the process repeats n times. Having found the solution only for the case of two steps, Pearson wanted an expression for the probability that the walker is a radius r from the starting point after n steps.
In the intervening 114 years, the random walk—or, more colorfully, the drunkard’s walk—has been applied to such diverse fields as ecology, economics, computer science, biology, chemistry, and physics, and it helped produce the art on the cover of this issue. Physicists use the random walk to model diffusion, Brownian motion, polymers,...
