Others have already explained how it demonstrates emergence quite well; I’d just like to add on that the game of life is not actually particularly important. While it does demonstrate the important concept that simple rules can lead to complex behaviors, there are plenty of other systems that also do this. Even the game’s inventor, the great John Conway, has stated in interviews that he doesn’t view the game as particularly interesting compared to the rest of his work.
It’s mostly just popular as a cultural phenomenon in the math and computer science community. It’s a fun challenge for programmers to try to implement and so they’ve made countless versions of it all over the internet.
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