Motivated by this comment I made on HN, reproduced further, I thought about making a all-in-one page of links concerning various experiments with quines in chemlambda. There are too many for one post though. In the Library of chemlambda molecules about 1/5 of the molecules are, or involve quines.

[EDIT: see the first post Quines in chemlambda from 2014]

If you want to see some easy to read (I hope) explanations, go to the list of posts of the chemlambda collection and search for “quine”. Mind that there are several other posts which do not have the word “quine” in the title, but do have quine-relevant content, like those about biological imortality, or about senescence, or about “microbes”.

There’s a book to be written about, with animated pages. Or a movie, with uniformised style simulations. Call me if you want to start a project.

Here is the comment which motivated this post.

“One of the answers from your first link gives a link to this excellent article

https://link.springer.com/chapter/10.1007%2F978-3-540-92273-…

on “autocatalitic quines”. The Introduction section explains very nice the history of uses of quines in artificial life.

There are some weird parts though in all this, namely that we may think about different life properties in terms of quines:

1) Metabolism, where you take one program, consume it and produce the same program

2) Replication, where you take one program, consume it and produce two copies.

But what about

3) Death

I thought about this a lot during my chemlambda alife project, where I have a notion of a quine which might be interesting, seen the turn of these comments.

A chemlambda molecule is a particular trivalent graph (imagine a set of real molecules, the graphs don’t have to be connected), chemical reactions are rewrites, like in reality, when if there is a certain pattern detected (by an enzyme, say) then the patern is rewritten.

There are two extremes in the class of possible algorithms. One extreme is the deterministic one, where rewrites are done whenever possible, in the order of preference from a list, so that the possible conflicting patterns are always solved in the same way. The other extreme is the purely random one, where patterns are randomly detected and then executed or not acording to a coin toss.

Now, a quine in this world is by definition a graph which has a periodic evolution under the deterministic algorithm.

The interesting thing is that a quine, under the random algorithm, has some nice properties, among them that it has a metabolism, can self-replicate and it can also die.

Here is how a quine dies. Simple situation. Take a chemlambda quine of period 1. Suppose that there are two types of rewrites, the (+) one which turns a pattern of 2 nodes into a pattern of 4 nodes, the other (-) which turns a pattern of 2 nodes into a pattern of 0 nodes (by gluing the 4 remaining dangling links in the graph).

Then each (+) rewrite gives you 4 possible new patterns (one/node) and each (-) rewrite gives you 2 possible new patterns (because you glued two links). Mind that you may get 0 new patterns after a (+) or (-) rewrite, but if you think that a node has an equal chance to be in a (+) pattern or in a (-) pattern, then there is twice as possible that a new pattern comes from a (+) rewrite than from a (-) rewrite.

Suppose that in the list of preferences you always put the (+) type in front of the (-) one. It looks that in this way graphs will tend to grow, right? No!

In a quine of period 1 the number of (+) patterns = number of (-) patterns.

Hence, if you use the random algorithm, the non execution of a (+) rewrite is twice more probable to affect future available rewrites than the non-execution of a (-) rewrite.

In experiments, I noticed lots of quines which die (there are no more rewrites available after a time), some which seem immortal, and no example of a quine which thrives.”