Recently Niemeyer, Pietronero, and Wiesmann (ibid., vol.52, p.1033, 1984) studied a stochastic model of dielectric breakdown. They examined the fractal character of dielectric breakdown patterns in two dimensions and showed that when the breakdown probability is taken to be proportional to the local electric field (p varies as Eeta , eta =1) the theoretical pattern has a Hausdorff dimensionality D of 1.75+or-0.02, in apparent agreement with the experimental value of 1.7. However, the simulations were done with a two-dimensional Laplace field, while in the experiment the field equation was in fact three dimensional (3D), as noted by the authors themselves. Satpathy points out that indeed the dimensionality of the Laplace field has a large effect on the breakdown pattern. In fact, the Hausdorff D may be expected to increase when the dimensionality of the Laplace field is increased.
 

Physical Review Letters, 57 649-50, 1986.