Theory of self-reproducing automata (1966)
archive.org
archive.org
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.
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.
In Conway's game of Life, known replicators are very large (gliders that destroy the original don't count as replicators) and randomly generating one of those would be take astronomical timescales. It's possible that there are smaller replicators.
In Highlife (slight rule variation) there is replicatior withing in 6×6 box. There are only 2^36 different states in 6x6 box. With random sampling it would take some time but would eventually emerge.
But I was deliberately browsing variants of Conway’s rule that supported the glider at least and maybe some of the other familiar objects.
Randomly initialized life quickly collapses
into stable structures, most of the time.
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.
https://archive.org/details/theoryofselfrepr00vonn_0/page/31...
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_universal_construc...