I've been trying to figure out how to create a random mesh -- or a random tree pattern -- or a random web pattern. I know don't have the correct terminology

.
Of course it doesn't have to be in a circle. I played around with the tree generator but it doesn't seem to be suitable for this application. Are there any extensions out there that does something like this? I'd be happy even with some process that created a regular pattern which I could then manipulate.
Any thoughts?
Thanks!