Nowhere‐differentiable attractors

The notion of nowhere‐differentiable attractors is illustrated with four prototype equations, that is, maps of invertible type. Four classes of nowhere‐differentiable attractors can be distinguished so far: the (nongeneric) continuous‐nonchaotic‐nonfractal type; the (nongeneric) continuous‐fractal type; the (generic) singular‐continuous‐fractal type; and the (generic) continuous‐fractal‐in‐a‐projection type. the history of all four classes is linked with the name of J. A. Yorke in different ways. Even though continuous fractal nowhere‐differentiable attractors do not exist genetically, the hypothesis that the fractal geometry of nature may be a consequence of the fact that nature is a differentiable dynamical system is strengthened. Attractors with nowhere‐differentiable generic projections can mimic the whole richness of fractal pictures. © 1995 John Wiley & Sons, Inc.