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Since BrainFuck is used in Computational Life: How Well-formed, Self-replicating Programs Emerge from Simple Interaction—highlighted in a recent YouTube video by Sabine Hossenfelder: Random Code Can Learn to Self-Replicate, New Study Finds—I thought that you might be interested in this paper.
From the abstract:
We show that when random, non self-replicating programs are placed in
an environment lacking any explicit fitness landscape,
self-replicators tend to arise. We demonstrate how this occurs due to
random interactions and self-modification, and can happen with and
without background random mutations. We also show how increasingly
complex dynamics continue to emerge following the rise of
self-replicators.
And, surprisingly,
Finally, we show a counterexample of a minimalistic programming
language where self-replicators are possible, but so far have not been
observed to arise.
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