For instance, the Koch Snowflake has a infinite perimeter but a finite area. Fractals occur frequently in nature, such as in the branching of trees and coastlines, which display equivalent patterns at all scales. An attractor describes the behavior of a dynamic system in a basin of attraction. Some attractors show a steady state, where any starting point will eventually converge to a single point, while other attractors are periodic, circling around in the same pattern. The most interesting type of attractor is the strange attractor, which describes some non-linear systems.
Strange attractors act like normal attractors in that they are confined to a finite area.
The path that they describe, however, is infinite, and keeps circling around, never reaching the same spot twice. Sometimes a strange attractor will exhibit a fractal-like structure. They are also sensitive to initial conditions, which means that even a small change at the start can produce completely different results. The study of artificial life has become more important. For example, researchers have simulated bird flocking and ant colony movement.