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Again, thank you for the ping, dear r9etb! I thoroughly enjoyed the article (emphasis mine:)

The theory suggests the existence of a state space (the set of all possible states of the universe), within which a smaller (fractal) subset of state space is embedded. This subset is dynamically invariant in the sense that states which belong on this subset will always belong to it, and have always belonged to it. States of physical reality are those, and only those, which belong to this invariant subset of state space; all other points in state space are considered “unreal.” Such points of unreality might correspond to states of the universe in which counterfactual measurements are performed in order to answer questions such as “what would the spin of the electron have been, had my measuring apparatus been oriented this way, instead of that way?” Because of the Invariant Set Postulate, such questions have no definite answer, consistent with the earlier and rather mysterious notion of “complementarity” introduced by Niels Bohr.

The fractal geometric structure is the key to his postulate, namely the self-similarity but with an invariant state at the root.

The Mandelbrot Set is probably the most famous example of a fractal.

Lurkers: click on any point in the graphic on the link to zoom in and examine the self-similarity.

In the Invariant Set Postulate, one of the states would be real and all the others unreal. He doesn't tell us how he intends to isolate/identify the invariant, but it does appear logical on first blush that one state must be real for all the others to be similar to (or illusions of) it.