Hmm, thinking about that I don't really have many. I thought esoteric programming languages are a good source of them, but truly exotic ones turn out to be surpringly rare.

Cellular automaton is vastly popular as a concrete mechanism for rule-based programming (PuzzleScript being a good example), reversible computing is no longer interesting because of quantum computers and perhaps homomorphic encryption, probablistic programming is a large enough niche that it was never exotic, circuitry-based declarative programming is not even a niche (cf. HDLs), self-modification as a single control mechanism has been tried multiple times throughout the history (often combined with string rewriting paradigm, which itself has been even more popular than self-modification), ... The list goes on and on.

Probably the most exotic concept that I have ever seen is a multi-dimensional control flow (most famously Befunge [1], with some other lesser-known precedents), but there has been several programming games making use of that. Gravity-based programming [2] and the Infinity Machine [3] might be interesting if you allow hypothetical ideas.

[1] https://esolangs.org/wiki/Befunge

[2] https://esolangs.org/wiki/Gravity

[3] https://www.chiark.greenend.org.uk/~sgtatham/infinity.html