Fractal Analyses of Simulated Fish School Movements and Video-Recorded Sardine Movements

Fish schools behave like a single organism and offer a considerable survival advantage. In our simulations, the fish school is well organized and behaves like a single creature depending solely on the interactions among individuals without having any director fish. This kind of system can be said as the typical one of "Complex Systems". We make clear the validity of fractal analyses to evaluate fish school movements through evaluation of both the simulated movements and the real sardine movements taken by video tape. The analyses showed that we need two kinds of fractal dimensions (D$_1$, D$_2$) to fit to the observations; the one(D$_1$) corresponds to smaller coarsening levels and D$_2$ does to larger coarsening levels. The double linear analyses in ...