Abstract: Measurements of fine-grained dolerites by optical automatic image analysis are used to illustrate the effects of magnification and resolution on the values obtained for grain ‘size’, grain boundary length, surface area per unit volume, and other parameters. Within the measured range of optical magnifications (× 26 to × 3571) and resolutions (1.20 × 10−3 cm to 8.50 × 10−6 cm), it is found that the values of all grain parameters estimated by chord size analysis vary with magnification. These results are interpreted in terms of the concepts of ‘fractal dimensions’ introduced by Mandelbrot (1967, 1977). For some comparative purposes the fractal relationships may be of little significance as relative changes of size, surface area, and other parameters can be expressed adequately at given magnification(s). But for many studies, for instance in kinetics of grain growth, the actual diameter or surface area per unit volume is an important dimension. The consequences are disconcerting and suggest that it may be difficult in some instances to specify the ‘true’ measurements of various characteristics of fine-grained aggregates.