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Self-Reproducing Cellular Automata (johndcook.com)
72 points by chmaynard 14 days ago | hide | past | favorite | 18 comments



(not directly related to the article) The cellular automata in the article is a discrete one. For those interested, there are also "continuous" automata https://www.youtube.com/watch?v=KJe9H6qS82I.


Not an expert here but what is the relationship between by this and Von Neumann's "Self Replicating Machines"? [0]

[0]: https://en.m.wikipedia.org/wiki/Self-replicating_machine


von Neumann's approach was to define a "universal constructor", with a programmable "arm" for altering cells. He came up with a complicated set of cellular automaton rules which allow such a universal constructor. Then he came up with a "program" for the constructor which, when executed, would create a copy of the universal constructor and of the program.

This was all meant to be in analogy to the physical world, where such a constructor could be used to build almost anything, perhaps operating at the atomic-scale.

It turns out that we can get much simpler self-replicators if we (a) ignore the "universal constructor" ability, and only focus on self-replication; and (b) choose cellular automaton rules which make self-replication easier, rather than using cells to encode "programs". This approach gives things like Langton's Loops https://en.wikipedia.org/wiki/Langton%27s_loops

The self-replicating property described in the article seems like an extreme form of this approach: the rules are so tailored for replication that they can't do anything else.

Of course, making such simplifications sort of defeats von Neumann's original purpose, since such highly-tailored rules are less "realistic", and hence don't particularly help us build physical self-replicators; and even if we could, they wouldn't be particularly useful without the "universal constructor" ability.


> Of course, making such simplifications sort of defeats von Neumann's original purpose

Yes. In von Neumann's last book "Theory of Self-Reproducing Automata", he thought about machines having viable offspring. This was more than a trick with patterns. He had invented the architecture of working computers, and was now moving on.

As a math grad student at Harvard around 1980, the wine flowed freely on Friday afternoons. I nevertheless headed over to the biology department, where cannabis-fueled discussions centered on work like von Neumann's.


Happy to see Chris Langton mentioned. He is often strangely neglected. Here is the transition table for Langton Loops:

https://github.com/GollyGang/ruletablerepository/blob/gh-pag...


If our universe is just one big cellular automaton (that's what Stephen Wolfram claims in his physics project) then one would wonder if we see a similar effect in real life.

Maybe the universe just doesn't use the right rule though.


Stephen Wolfram did not invent this

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


> If our universe is just one big cellular automaton (that's what Stephen Wolfram claims in his physics project) then one would wonder if we see a similar effect in real life.

We ourselves and everything around us would be that evidence...it's finding out if everything is made up of cellular automata that's the hard part.


I'm talking about this self-replicating effect in particular. In some distance far far away, there'd be some instance of me exactly identical and behaving exactly identically including writing these words right now.

Or, more generally, some superimposed versions of me partially overlapping, as can be seen with those overlapping Es in the original article.


>I'm talking about this self-replicating effect in particular. In some distance far far away, there'd be some instance of me exactly identical and behaving exactly identically including writing these words right now.

Maybe.

>Or, more generally, some superimposed versions of me partially overlapping, as can be seen with those overlapping Es in the original article.

Maybe - it depends on the complexity of not just you but everything around you. There may be billions of similar yous around you, with some variation based on their history, but it's not close enough 'you' for your arbitrary definition.

I guess what I'm saying is, it really depends on how it all works. The interactions of different cellular automata can still give rise to incredible complexity that might make identical yous very difficult or impossible. Twins have similar circumstances to a high degree but even they can be different physically and are always different experimentally.

It's complicated.


This effect also happens with continuous models, as there is only a finite number of quantum states in any finite subset of space. In fact, any notion of infinite space will virtually guarantee that there are exact copies (infinite copies) of you and me doing what we do now. But it's basically only a philosophical question since we only have access to our observable universe.


DNA copying is kinda similar.

Also look into fractals, since they are self similar.


> If our universe is just one big cellular automaton

Aren't cellular automata deterministic, but the universe is non-deterministic at the quantum level?


Just like life in a cellular automata world could figure out the rules behind cell replication and destruction, they could never peer underneath at the mechanism driving it all. For us, is there a level underneath the quantum level? We can speculate (i.e. string and m-theory), but we may never find out because we're made of matter constrained by three spatial dimensions and our sensing equipment is similarly constrained. For an outside entity observing the universe, it may very well be deterministic, and what we see as quantum probabilities and non-determinism are simply limitations in our ability to build better testing equipment, because we can only work with what the universe provides to us (atoms and particles).


your comment made me think of this comic: http://english.bouletcorp.com/2011/12/08/pixel-quantum/


Depends on who you ask. In the Everett interpretation, quantum mechanics is deterministic, and uncertainty about quantum mechanical measurements arises from indexical uncertainty (“which observer am I?”) rather than fundamental randomness.


Why can't cellular automata rules contain a quantum_rand()? [1]

Most games and simulations contain RNG's to make things interesting, quantum uncertainty seems to look very similar to my naive self.

1. https://content.wolfram.com/uploads/sites/34/2020/07/random-...





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