In this paper the radiation from a geometrically fractal (i.e., arbitrarily irregular) discharge channel is investigated from the point of view of engineering applications of fractal geometry. Numerical results are presented for lightning return stroke radiation, which demonstrate that the time waveform of radiated field (in the Fraunhofer region) is a fractal, and within the framework of employed approximations, it has the same fractal dimension as the channel path. Some implications of this finding are discussed along with the limitations of the model. ¿ American Geophysical Union 1994