An interesting option is rod logic, which is the mechanical equivalent to a PLA (programmable logic array).

https://www.jamiekawabatarobotics.com/?p=40

I have had an interest in building a mechanical computer for a long time. It has not ever gotten farther that some research into what route to take. There are lots and lots of simple logic mechanisms (many, many in use in real world applications). It can go as far and be as capable as you have time for.