Random walks and mobile entities

Random walks are one of the most basic stochastic processes, and furthermore provide an obvious starting point for models of mobile entities. A wide range of variations on the basic random walk idea are presented, followed by examples where walkers interact with an environment, often by searching for resources. When many mobile entities interact with one another, an interest variation is models of flocking behaviour.

4.1 Random walks

This model implements a number of variations on the random walk including the lattice-based walk, the simple random walk, walks with different distributions of step lengths…

4.2 The correlation length effect in random walks

This model demonstrates how a correlated random walk, when consecutive steps are aggregated, reverts to a simple random walk without correlation but with a longer mean step…

4.3 Simon’s satisficing forager model on a lattice

This is a loose implementation of the model of resource search discussed in

4.4 Area searched by a ‘Simon forager’

Results from this model are used in figure 4.12 to demonstrate the relationship between movement tortuosity and search efficiency.

4.5 Foraging in a heterogeneous environment

This model demonstrates how the distribution of resource availability in an environment can strongly influence the characteristics of movement motivated by exploitation of…

4.6 The effect of environmental change on movement

This model shows how a changing environment can drive the characteristics of observed movement.

4.7 Flocking

A flocking model loosely based on ideas in