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I remember to this day the exact location I was when being introduced to construct hypercubes, to the exact bench in our uni cafeteria. It changed my understanding of multidimensionality completely.

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Thanks for that, i was initials skeptical i would understand but this very clearly resembles the candidate paths for walkers in variatonal monte carlo simulation of spin systems. The edge set can be different, requiring "half filled" and flipping both a 1 and a 0 simultaneously. I'd not thought of these processes in terms of a graph, much less graphs which denote very high dimensional cubes with strange edges.

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