Tetration in busy-beaver Turing machines and in Conway's Game of Life:
https://www.sligocki.com/2022/06/21/bb-6-2-t15.html
https://cp4space.hatsya.com/2022/06/23/tetrational-machines/
https://btm.qva.mybluehost.me/telling-the-tale-of-two-tetrations/