This Demonstration starts with a single branch and continues drawing branches at the ends of each previous branch. Going clockwise, branches are added except when a branch would collide with the end of an existing branch. Each step shows the result of attempting to add a branch to the end of each of the branches from the previous step.
This pattern can easily be drawn by hand and looks a bit like a fractal. The (almost) space-filling lattice of hexagons also resembles the structure of the nanomaterial graphene. Here is a link to a video of the branches being added one at a time in a circle.