Irradiating acrylic with x-rays gives an enormous amount of energy to the lattice bonds. Energy that wants to be released. With a lichtenburg figure, such as is used here [made by Danielle Smith in the Chemical Engineering lab], that energy is released by a single tap of a nail onto the edge.
The fanning out pattern, tree-like and fractal, is a result of the bond-breaking cascade attempting to find a minimum energy path to settle into. From lightning to trees and beyond, this pattern is evident in nature around us.