The term branching structure is commonly used in the graph theory to describe a type of hierarchy.
Edit: The best I could come up with after you edited your question is to describe it as something-shaped, for example lightning-shaped. No term that I can remember of apart from e.g. specific computational algorithms does incorporate the randomness.
Second edit: I have just remembered the word stochastic or pedesis, while the latter is another term for Brownian movement. Considering these terms, you may utilise something like stochastic branching structure if you need to appear appealing. That is my current limit, I am afraid. :-)