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Not sure what any of this means but pretty cool that you used analogous in a sentence like that

Maybe. I mean, mathematically, both are Iterations. Both can converge towards a final state or get stuck in a loop (a so called attractor). But that's about it.

I don't think so. Game of Life is Turing Complete, and to highly oversimplify what Turing completeness is, it basically means it can theoretically perform any computation your computer can from given instructions. So when a pattern in a Game of Life ends up in a loop, you are actually instructing it to do so, not much different than writing while (true) {} in a computer program for example. While here, it's just two pages ultimately linking to eachother.

...yes? Well, at least there's valid definitions of "analogous" that make this true: Hypertext links form a directed graph, loops form, well, cycles in that graph, and executions of game of life can be mapped onto a directed graph, and that graph can contain cycles, just as with hyperlinks without any out-edges escaping those cycles. Executions, plural, if you only use one the graph will have only one out-edge per node and either be infinite, or have one back-edge. Rather degenerate, you'd call it a (repeating) sequence instead of a graph to not make things unnecessarily complicated.

Not very meaningful though as wikipedia articles and game of life aren't isomorphic, at least to my knowledge. If they were isomorphic you'd actually have interesting mathematics at hand.

They're both... terminally loopy graphs, that's it (I just made up that term there's probably a proper one). Also the ones "ending" in philosophy also end in a loop, it just happens to include philosophy.