Fractal evaluations of fish school movements in simulations and real observations

Abstract

Fish schools behave like a single organism, and this offers considerable survival advantages. In our simulations, a fish school is well organized, without a leader, and behaves like a single creature depending solely on the interactions among individuals. This kind of system can be said to be typical of “complex systems.” In this article, it is shown that fractal evaluation is useful to understand the features of fish school movements. We make clear the validity of fractal analyses to quantify fish school movements through evaluations of simulated fish school movements andsardine movements. These fractal analyses show that we need two different fractal dimensions (D ₁,D ₂) to understand the features of fish school movements:D ₁ corresponds to thesmaller coarsening levels, andD ₂ corresponds to thelarge coarsening levels. The linear analyses in log-log space give an excellent fit with both the simulated movements and the sardine school movements. In approaching complex systems or complex behaviors, fractal analyses have attracted wide attention in mathematics, physical sciences, and information science. The fractal evaluations here convince us that we are coming close to understanding the structure of complex movements of animals.