Perturbed quine experiment

I use as a tool the page find a quine.  You saw in the post 10-node quine can duplicate that indeed in rare situations the simple 10-node quine can indeed reproduce spontaneously. You can see for yourself: choose “original 10_nodes quine” from the menu, hit the  “start” and if it dies hit “reload” and “start” until you witness a reproduction.

In this post I want to show you another phenomenon, which is logical after you see it, but perhaps is surprising at first sight.

Recall that a chemlambda quine is a graph which has a periodic evolution under the greedy algorithm of rewrites. It is of course interestign what happens under the random reduction algorithm. Maybe this definition should be changed?

What if we modify the definition by saying that a quine is a graph which can evolve into a graph which itself is a quine according to the original definition. Then, OK, but it may be the case that a graph, even one of a quine according to the original definition, has the following weird property: it can evolve into two different quines. Namely there are two different reduction paths which, each, lead to a quine.

Here is a proof that this is happening for the quine which you can load from the menu as “10 nodes quine 2 = [A-L-FI-FO 245013]”.

First, what does “= [A-L-FI-FO 245013]” means? If you look in the menu, there is the option “new random 4 nodes graph A-L-FI-FO” which generates one of the 720 graphs with 4 nodes A, L, FI, FO. Then there are some examples of such graphs which evolve into  quines, my favorite being the remarkable “quine from [graph A-L-Fi-FO 243501]”.

Then “10 nodes quine 2 = [A-L-FI-FO 245013]” means that this particular 10 nodes graph evolves into the same quine as the one which is obtained from [graph A-L-Fi-FO 245013]. So there’s one quine. (For the notation [A-L-FI-FO 245013],  notice that 245013 is a permutation of 012345 which describes in which way the nodes A, L, FI, FO are connected. You can see how is done, and especially why there are 720 such graph, if you look in the molLib.js at the lines after

case random_egg_A_L_FI_FO

)

The second quine can be obtained by a perturbation. Indeed choose “10 nodes quine 2 = [A-L-FI-FO 245013]” from the menu and start to perturb it with the mouse:

10-nodes-quine-2-perturbed-s1

Then press “start”

10-nodes-quine-2-perturbed-s2

That’s a different quine. Indeed, most of the time you get the first one which is small:

10-nodes-quine-2-perturbed-s3

You can see it by doind simply “reload” and “start”.

Only rarely you’ll see the bigger quine.

Other surprises wait for you, and for me too.

 

 

 

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