Any algorithm can be recast as being "self-modifying", "aperiodic" etc. We don't gain any security by doing so. It's just a choice of how to model what the algorithm does which makes it harder to analyse. Sure, it makes it harder for an adversary to analyse too, but only if they stick to the author's way of modeling what the algorithm does - as opposed to finding a more concise description of what it does.
That's the key distinction. This isn't just a complex function, but a programmable machine that enables new capabilities.
For example: verifiable, time-locked proof of computation on a secret program. A standard hash or ZK-SNARK can't prove the when or how long of a simulation. Our model can.
The execution of the secret program leaves an irreversible "scar" on a one-time-use Labyrinth. The final state of this scarred structure is a commitment to the entire computational history, which is then time-locked by a Verifiable Delay Function (VDF).
The proof isn't just an output; it's the final, mutated state of the Labyrinth itself. An adversary can't find a more concise model because the history of the computation is inseparable from the proof.
