Example of five random walk simulations in a 2-dimensional integer lattice. As a more mathematical application, the value of pi can be approximated by the usage of random walk in agent-based modelling environment. Various types of random walks are of interest, which can just walk on by pdf in several ways. The time parameter can also be manipulated.
A popular random walk model is that of a random walk on a regular lattice, where at each step the location jumps to another site according to some probability distribution. This walk can be illustrated as follows. A marker is placed at zero on the number line and a fair coin is flipped. If it lands on heads, the marker is moved one unit to the right. If it lands on tails, the marker is moved one unit to the left. With five flips, three heads and two tails, in any order, will land on 1.