Fractal

The geometries of shores, rocks, plants, waves, hydrodynamic flow, organism trajectories, and many other natural phenomena are important in different scientific disciplines, and each field tends to adapt specific concepts to describe the complexity of Nature. Ecological models often approach natural shapes as simple geometrical approximations. Lakes are approximated as circles, particles as spheres, patches as squares and rectangles, and trees as cones. Many patterns and shapes in Nature, however, are so irregular and fragmented that they present not simply a higher degree but an altogether different level of complexity, as compared with Euclidean approximations. Curves, surfaces, and volumes in Nature can thus be so complex that ordinary measurements become meaningless.

Many natural phenomena have a nested irregularity and may look similarly complex under different resolutions. Although this nested structure, referred to as scale invariant, could be thought of as an additional source of complexity, it becomes a source of simplicity in fractal geometry.