Interactive Animation of Shoals Based on Mathematical Ecology

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In this research, we have developed an interactive visual simulation of ecosystems, in which fish schools are visualized with changing the population. In computer graphics, a computer model of coordinated animal motion, which is called the boid algorithm, is a well-known technique and is used in many programs, such as computer games. Although the realistic visualization of flocking creatures is possible using the boid algorithm, the birth, growth, and death of creatures are not taken into consideration. Mathematical ecology deals with population dynamics, the fluctuations of the number of individuals of different species. We developed a interactive visual simulation system in which the schools of fish are formed by the boid algorithm and the numbers of fish are changed with time through their birth, growth, and death based on the Lotka-Volterra's equations. Two kinds of Lotka-Volterra's equations are dealt with: (1) competing two species model and (2) predator-prey model. To add the interaction by the user, the user can change the number of individuals by placing a circular net in the field to capture them and henceforth decreasing the number of individuals. After changing the population, the user can visually see its effect.