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All objects considered previously have been identified by specifying that some measure distributed on them is uniform: For example, the concentration on an isoconcentration contour is by construction the same everywhere. A description of such sets is then the same as that of the measure living on them. On the other hand, consider an instantaneous realization of the scalar dissipation rate X~[grad C] 2; the set here is the space marked by the scalar, and the measure living on it is X. As shown in Figures l4a (see color insert) and 14b, this measure is highly spiky in nature. The geometry of the set on which X is distributed is thus only a part of the picture, and a more detailed machinery is necessary to describe X itself. As a second example, consider Figure 15, which shows onedimensional sections of a component of energy dissipation in a laboratory flow at moderate Reynolds number and in the atmosphere at higher …