Here we have a random search tree. We start with an initial point. It then selects a point at random in its environment and figures out which node in the tree is closest to it. Then a line segment is drawn of a certain length that lies on the same line defined by these two points. This process then repeats with the new expanded tree.

These can be used in path finding for robotics, not to mention that they just look cool.

You can click anywhere in the applet to define a new starting point.