In September 2023, Inna Zakharevich of Cornell University...

In September 2023, Inna Zakharevich of Cornell University and Thomas Hull of Franklin & Marshall College showed that anything that can be computed can be computed by folding paper. They proved that origami is “Turing complete” — meaning that, like a Turing machine, it can solve any tractable computational problem, given enough time.

https://www.quantamagazine.org/how-to-build-an-origami-computer-20240130/

Flat origami is Turing Complete
https://arxiv.org/abs/2309.07932