There's a variant of Conway's Game of Life called Wireworld which is turing complete. The idea is that there is a "signal" traveling along a wire. You can try it here, try programming a calculator if you have a lot of hours to spare: https://xalava.github.io/WireWorld/
Back in the day Golly was the best software for playing around with Game of Life variants, might still be true: http://golly.sourceforge.net/
Talking about WireWorld, we're making a game that involves drawing circuits. It's written in Unity and will feature 20ish levels, but we have a very early web-based prototype: https://charperbonaroo.github.io/bls/#0
Back in the day Golly was the best software for playing around with Game of Life variants, might still be true: http://golly.sourceforge.net/