The fractal dimension of cathode spots occurring in the discharge of a highcurrent vacuum arc thruster (VAT) are determined according to the Minkowski-Bouligand method. Photographs taken during operation of a 30 W VAT allowed observation of spots distribution over the surface depending on the cathode material. A machine learning model as well as a heuristic analysis permit to outline that work function, cohesive energy and ionization energy of the cathode material are the main driver in the magnitude of fractal dimension and total surface area covered by the spots.