The hypothesis is presented that fractal geometry, and the fractal dimension in particular, is likely to be a more useful method of image analysis in histopathology than the use of regular Euclidean geometry. The concept of the fractal dimension is described and it is suggested that many human tumours have a fractal structure over a wide range of scales. It is postulated that the fractal dimension will be useful in discriminating between different diagnostic categories and may also allow more precise prognostic stratification within single diagnostic groups.