I have been reading up on the Amish for one chapter of the book on legal systems very different from ours that I'm currently working on. They provide an example of what I think of as an embedded legal system—a group that is under the authority of an external legal system, but also has its own legal system which it succeeds in enforcing on its members. Other examples are modern gypsies and Jewish communities during the diaspora, which were often given the right to impose Jewish law on their members by their gentile rulers.
It occurred to me that one could view the Amish as a working example of a form of anarchy. It is a very strange form, since the rules that the Amish are under are considerably more constraining—including rules on what styles of clothing they can wear, rules against owning automobiles or flying on airplanes, and much else—than the rules the rest of us are under. But those rules are all voluntarily accepted, and the system that generates them may reasonably be viewed as a competitive system of private law.