Two-dimensional random walks The examples of random walks we have studied have been one-dimensional. They have modelled a single variable: global mean temperature. This idea can be extended to two-dimensional random walk models, which have many applications in biology, including modelling the foraging behaviour of ants, modelling the movement of bacteria and cell organelles under molecular collisions (Brownian motion), A simple two-dimensional random walk model takes the form H+-H+X and V+1-V, where . X and Y are two random variables that both have normal distribution and mean zero, . H is the horizontal (i.e., z) co-ordinate at step i, and . V, is the vertical (i.e., y) co-ordinate at step i. We assume that movement in the horizontal and vertical directions do not influence each other Two-dimensional random walks The examples of random walks we have studied have been one-dimensional. They have modelled a single variable: global mean temperature. This idea can be extended to two-dimensional random walk models, which have many applications in biology, including modelling the foraging behaviour of ants, modelling the movement of bacteria and cell organelles under molecular collisions (Brownian motion), A simple two-dimensional random walk model takes the form H+-H+X and V+1-V, where . X and Y are two random variables that both have normal distribution and mean zero, . H is the horizontal (i.e., z) co-ordinate at step i, and . V, is the vertical (i.e., y) co-ordinate at step i. We assume that movement in the horizontal and vertical directions do not influence each other