In the above video they've charged an acrylic block by aiming an electron beam into it and injecting it with high speed particles. These particles slow down and become trapped in it, eventually building up a negative charge of millions of volts. When sharply tapped with a conductive object this voltage will discharge, leaving a pattern known as an Lichtenberg figure or an electron tree. The sparks you see after the original discharge are secondary discharges that can continue to occur for several minutes.
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Lichtenberg patterns can also be found in the grass at the point of a lightning strike. I live in Florida and I've heard of them being seen on golf courses in the area. Finally, sand at the point of the strike can be fused into underground and the resultant fragile, glass-like structure is called a fulgurite.