ulate (Grassberger, 1981). This is a dust-like region, which when endlessly dilated looks like the same dust. Some mathematicians call these objects “Lebesgue points” because even though at low magnifications when they look rather solid, they are not. Composed of points, they have topological measure zero

nd in a wide variety of attractors, though in each case the parameter space in which they are located is so small (in point set topology also called “Lebesgue measure zero”) that they are very difficult to locate and therefore have little chance of being physiologically significant. This constrasts with a