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I believe weregiraffe is referring to this[1][2]. Conway's Game of Life is a 2D "world" with 4 rules that define the "physics" in that world, and someone made a Turing Machine in it.

[1] https://www.ics.uci.edu/~welling/teaching/271fall09/Turing-M...

[2] http://www.rendell-attic.org/gol/tm.htm

https://en.wikipedia.org/wiki/Rule_110 A Turing Complete 1-dimensional cellular automaton.

Also Conway's Game of Life is a rabbit hole you could literally spend your whole life studying.

That is life like but I would not call it life.

That's the issue with this question. What is life? Common definitions would never think to consider anything other than things in our 3D physical world.

Can Life Exist in 2 and 1 Dimensions? Sure, if we're willing to define "life" generically enough. If not, then no.

Since the universe may be encoded on lower-dimensional boundary, that means that you are not alive, per your definition:

https://en.wikipedia.org/wiki/Holographic_principle

One can simulate life using Turing machine.