Toward a better understanding of fractality in nature

Abstract Boundaries of coexisting attractor basins are a common source of fractal structures in discrete maps. Chaotic attractors in continuous systems of ordinary differentiable equations also have a fractal microstructure. A generation mechanism for self-similar fractal boundaries is proposed, which gives a closer connection between “chaos” and “fractals.” We discuss the role of analyticity, critical points, chaotic forcing, and bistability as some of the elements needed to answer the major, still unresolved question of whether nature is fractal because, or in spite of, the existence of differentiable systems.

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