
Theory of self-reproducing automata (1966) - HNLurker2
https://archive.org/details/theoryofselfrepr00vonn_0
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MattConfluence
I have an anecdote about this book!

I wrote my master's thesis about some cellular automata experiments. This was
in 2016, so in the 50th anniversary year of the book. While doing background
research I checked my university library's online database and found they had
a copy of this book in storage off-site. So I had it retrieved and checked it
out. Perfect condition. On the little card on the inside of the cover that
shows previous borrowers there was one name and date, some time in the 70's,
around the time my dad attended the same university.

While it is possible there were more borrowers of the book that just weren't
noted on the card (I myself was registered in a digital system of course),
there can't have been many, since there was so little wear and tear. Made me
wonder what other "treasures" are lying around libraries around the world,
waiting generations between each time someone checks them out.

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no_gravity
I wonder if there are estimates out there about how long a randomly generated
game of life instance of NxN cells will take until a self-reproducing
structure appears. An event that we have not witnessed so far.

Somehow I feel it is related to the question how likely it is for a
planet/galaxy/universe to breed life. An event that we have "witnessed" just
once so far.

One way to divide it into two estimates:

c = Number of cells of the smallest possible self-reproducing structure

i = Number of new structures that are created on average for each iteration

Then a rough guess could be that it takes 2^c/i iterations.

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whatshisface
Randomly initialized life quickly collapses into stable structures, most of
the time. Modeling it as if it continually permuted randomly though possible
states does not fit how it really tends to work in practice.

~~~
no_gravity

        Randomly initialized life quickly collapses
        into stable structures, most of the time.
    

Is this true? That would be a very profound finding. Any papers that discuss
this?

Looking at a random game of life with 10^6 cells, I get the feeling that it
will not loop for a long time.

Maybe it is a misunderstanding. I do not mean to find a self-replicator of
size c in a field of size c. I would expect that the field is big. Very big.
Let's say 10^80 cells. That is the estimate for the number of atoms in the
universe. The self replicator would be way way smaller. One manually
constructed replicator (Gemini) is just 10^7 cells. And that is certainly not
the smallest replicator possible.

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DonHopkins
Page 312 has the sexy playboy centerfold spread of John von Neumann's 29 state
transition rule:

[https://archive.org/details/theoryofselfrepr00vonn_0/page/31...](https://archive.org/details/theoryofselfrepr00vonn_0/page/312)

Ordinary, Confluent: C<ee'>, Number: 4, Received conjunctively from T<0ae>
directed toward it; emits with double delay to all T<uae> not directed toward
it. Killed to U by T<1a1> directed toward it; killing dominates reception.

[https://en.wikipedia.org/wiki/Von_Neumann_cellular_automaton](https://en.wikipedia.org/wiki/Von_Neumann_cellular_automaton)

[https://en.wikipedia.org/wiki/Von_Neumann_universal_construc...](https://en.wikipedia.org/wiki/Von_Neumann_universal_constructor)

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cellular
[https://youtu.be/gaFKqOBTj9w](https://youtu.be/gaFKqOBTj9w) A new kind of
automata.

~~~
thecupisblue
Oh shit. Love that paper. Wonder what it would end up looking like in a 4D
torus.

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ericsoderstrom
Is there any finite initial condition for Conway's game of life that will
expand to fill an arbitrarily large area of the plane with density that does
not approach zero?

~~~
Isamu
The spacefiller is what you are looking for I think.

[https://en.m.wikipedia.org/wiki/Spacefiller](https://en.m.wikipedia.org/wiki/Spacefiller)

