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Ever since its foundations were laid nearly a century ago, quantum theory hasprovoked questions about the very nature of reality. We address these questionsby considering the universe, and the multiverse, fundamentally as complexpatterns, or mathematical structures. Basic mathematical structures can beexpressed more simply in terms of emergent parameters. Even simple mathematicalstructures can interact within their own structural environment, in arudimentary form of self-awareness, which suggests a definition of reality in amathematical structure as simply the complete structure. The absoluterandomness of quantum outcomes is most satisfactorily explained by a multiverseof discrete, parallel universes. Some of these have to be identical to eachother, but that introduces a dilemma, because each mathematical structure mustbe unique. The resolution is that the parallel universes must be embeddedwithin a mathematical structure, the multiverse, which allows universes to beidentical within themselves, but nevertheless distinct, as determined by theirposition in the structure. The multiverse needs more emergent parameters thanour universe and so it can be considered to be a superstructure.Correspondingly, its reality can be called a super-reality. While everyuniverse in the multiverse is part of the super-reality, the completesuper-reality is forever beyond the horizon of any of its component universes.

Reality and super-reality: properties of a mathematical multiverse