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"Turing completeness" is extremely orthogonal to complexity.

Being "Turing complete" only means that your thing supports unlimited recursion; or, in other words, that whatever objects it encodes can be arbitrarily large.

See: https://en.wikipedia.org/wiki/Rule_110

P.S. This also means that, technically speaking, the computers we use aren't Turing complete because they have RAM and storage limits.



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