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Hmmm... I wonder if these spectres are potentially a basis for a new form of cryptographic algorithms. Unique non-repeating sequences exclusively derived from a set of rules and an initial state in multiple dimensions sounds like a promising candidate.

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I'm not understanding why that's different than seeded random sequence or the sequential digits of any irrational number? The latter guarantees a non-repeating sequence and can be trivially generated with square roots.

The question is in reversibility. A typical PRNG is hard to exactly reverse, but easy to brute-force, given a few values from the sequence.

I think it may be way harder to brute-force a tiling, because the number of tiles grows quadratically relative to the distance from an initial configuration. I wonder how easy would it be to step back.

I think lattices are probably more secure though. It's a similar idea to tiling but you can run it in a huge number of dimensions, without having to change the underlying math.

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