alt Hacker NewsTwo of the most fascinating open questions about the Game of Life are in my opinion:
1. What is the behavior of Conway's Game of Life when the initial position is random? Paraphrasing Boris Bukh's comment on the post linked below, the Game of Life supports self-replication and is Turing-complete, and therefore can support arbitrarily intelligent programs. So, will a random initial position (tend to) be filled with super-intelligent life forms, or will the chaos reign?
There exist uncountably infinitely many particular initial configurations out of which a random one may be drawn, which makes this more difficult (a particular infinite grid configuration can be represented as the binary digits (fractional part) of a real number, spiraling outwards from a given center coordinate cell: 0.0000... represents an empty infinite grid, 0.1111... a fully alive infinite grid).
https://mathoverflow.net/questions/132402/conways-game-of-li...
2. Relatedly, does a superstable configuration exist? One that continues to exist despite any possible external interference pattern on its border? Perhaps even an expanding one?
https://mathoverflow.net/questions/132687/is-there-any-super...
Replies
Your first question is discussed in the book The Recursive Universe by William Poundstone (1984).
One of the chapters asks "what is life?". It considers (and rejects) various options, and finally settles upon a definition based on Von Neumann-style self-replicating machines using blueprints and universal constructors, and explains why this is the most (only?) meaningful definition of life.
Later, it talks about how one would go about creating such a machine in Conway's Game of Life. When the book was written in 1984, no one had actually created one (they need to be very large, and computers weren't really powerful enough then). But in 2010 Andrew J. Wade created Gemini, the first successful self-replicating machine in GoL, which I believe meets the criteria - and hence is "alive" according to that definition (but only in the sense that, say, a simple bacteria is alive). And I think it works somewhat like how it was sketched out in the book.
Another chapter estimated how big (and how densely populated) a randomly-initialized hypothetical GoL universe would need to be in order for "life" (as defined earlier) to appear by chance. I don't recall the details - but the answer was mind-boggling big, and also very sparsely populated.
All that only gives you life though, not intelligence. But life (by this definition) has the potential to evolve through a process of natural selection to achieve higher levels of complexity and eventually intelligence, at least in theory.
> the Game of Life supports self-replication and is Turing-complete, and therefore can support arbitrarily intelligent programs.
I think people will disagree about whether “Turing-complete” is powerful enough for supporting intelligence but let’s assume it does.
> So, will a random initial position (tend to) be filled with super-intelligent life forms, or will the chaos reign?
Even if it doesn’t, it might take only one intelligent life form for the space to (eventually) get filled with it (the game of life doesn’t heave energy constraints that make it hard to travel over long distances, so I don’t see a reason why it wouldn’t. On the other hand, maybe my assumption that all intelligent life would want to expand is wrong), and in an infinite plane, it’s likely (¿certain?) one will exist.
On the other hand it’s likely more than one exists, and they might be able to exterminate each other.
One problem is that, even though it is turing-complete, many practical operations are very difficult. Patterns tend towards chaos and they tend towards fading out, which are not good properties for useful computation. Simply moving information from one part of the grid to another requires complex structures like spaceships.
You might have better luck with other variants. Reversible cellular automata have a sort of 'conservation of mass' where cells act more like particles. Continuous cellular automata (like Lenia) have less chaotic behavior. Neural cellular automata can be trained with gradient descent.