 Although there is no universally accepted definition for strange attractors or fractal dimension among mathematicians, the more serious question is whether strange attractors and fractal dimensions are properties of our models only or also of actual-world systems. For instance, empirical investigations of a number of actual-world systems indicate that there is no infinitely repeating self-similar structure like that of strange attractors (Avnir, et al. 1998; see also Shenker 1994). At most, one finds self-similar structure repeated on two or three spatial scales in the reconstructed state space and that is it. This appears to be more like a prefractal, where self-similar structure exists on only a finite number of length scales. That is to say, prefractals repeat their structure under magnification only a finite number of times rather than infinitely as in the case of a fractal. So this seems to indicate that there are no genuine strange attractors with fractal dimension in actual systems, but possibly only attractors having prefractal geometries with self-similarity on a limited number of spatial scales. 