Cell surfaces and fractal dimensions

The perimeters of the surface membranes of some different cell types have been digitized from electron micrographs and the data analysed in order to discover whether the perimeter can be described by a fractal dimension, df. Micrographs obtained at various magnifications and subsequently enlarged by different amounts have been used. Values of df ranging from 1.02 to 1.34 were manifested over a scale length of about one order of magnitude. Values of df were independent of the magnification, and were the same for cells of the same type. Possible implications of these results are discussed.