Conway’s game of life (like many complex automatons) is Turing complete, which means that you can program in it, which means that you can program itself in itself.

This is the basis for Greg Egan’s 1995 scifi Permutation City, which is a fun read.

If you want to understand how this works in depth, there’s an explainer on youtube too: https://www.youtube.com/watch?v=Kk2MH9O4pXY