Local fractal dimension map and spectrum of discharge pattern in liquid

Discharge patterns in a liquid can be analyzed by multifractals. The growth mode of the pattern of discharge can also be classified using a global spectrum. It is, however, difficult to understand the curve of its global spectrum, because its spectrum loses information on the location of the pattern. A local fractal dimension map is proposed to analyze the development mechanism of a tree-like discharge and the local fractal dimension spectrum is also calculated from the map. Fourier transforms of the local fractal dimension map can be available to analyze branches of the discharge tree.