Stoneridge Engineering creates these Lichtenberg figures by using a particle accelerator to create a charge cloud inside of a highly insulating block of acrylic and then discharging that cloud by poking it with what is essential a nail in a board connected to ground. 

This grounding probe causes the substantial charge that's within the block to vaporize the plastic along it's path and creates these beautiful images in the process.

There a video of this discharge process here and you can buy your very own Lichtenberg Figures here!