An important scenario in the study of biological systems is the interaction between predators and their prey. This takes place amongst many species: shark/fish, fox/hare, ladybird/greenfly, mould/bacteria. A typical feature of a predator-prey cycle is the lapsed development of the population concerned: prey multiplies, predators multiply, prey is decimated, predators have insufficient food sources and population reduces...
A much more complex scenario develops, when the system is seen in a further spatial dimension, in which predator and prey are moving. Such a scenario is simulated here. Prey fish (red) are moving freely and aimlessly and are multiplying. Sharks (blue) are moving preferably in the direction of the prey fish, as they need these to survive and reproduce. Consequently, extremely complex patterns develop. For example, in this simulation one can change the swimming speed of the fish. If they are swimming faster than the sharks, then a waved pattern develops.