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The Dietz replicator (aka JD replicator) was found after random searches in the 9 billion family of graphs which you can also explore.

It is a chemlambda molecule with the property that it produces a finite, but random length string of application A and fanout FOE nodes.

It looks like this:

It has the code:

L 0 8 12^FI 1 2 0^A 3 4 14^FI 5 6 10^FOE 8 2 6^FOE 9 5 4^A 10 in 1^FOE 12 13 3^A 13 14 9^Arrow a1 in

If we let it reduce randomly, it can take random shapes, like this:



It can be used with any molecule obtained from a lambda term. Mind that the Dietz replicator does not represent a lambda term!

It will produce a finite but random number of pairs of the initial template, even if the template molecule itself reduces in the same time.

Indeed, let's glue the Dietz replicator to the 1-node molecule which represents the identity lambda term. The molecule obtained has the code:

L 0 8 12^FI 1 2 0^A 3 4 14^FI 5 6 10^FOE 8 2 6^FOE 9 5 4^A 10 in 1^FOE 12 13 3^A 13 14 9^Arrow a1 in^L a7 a7 a1

and it looks like this:



If we let it reduce randomly, it produces a random number of pairs of Id molecules, like this:



The same can be tried with the Omega combinator molecule. The molecule obtained has the code:

L 0 8 12^FI 1 2 0^A 3 4 14^FI 5 6 10^FOE 8 2 6^FOE 9 5 4^A 10 in 1^FOE 12 13 3^A 13 14 9^Arrow a1 in^L a2 a3 a4^FO a3 a5 a6^A a5 a6 a2^A a4 a7 a1^L a8 a9 a7^FO a9 a10 a11^A a10 a11 a8

and it looks like this:



Differently from the Id molecule, the Omega molecule is a chemlambda quine. That means it reduces forever, it does not have a final shape.

If we let the Dietz replicator + Omega to reduce randomly, it produces a random number of pairs of Omega molecules, which are all in various stages of reduction themselves, and they will continue to reduce forever! Snapshots look like like this:



The ability of this replicator is that it produces copies of active molecules, while they continue to function. This is a far harder to achieve property than just replication. But Nature can do this, for sure: living cells reproduce while they also continue to have a metabolism. In Nature there is no clear separation between functioning (metabolism) and pure replication.

You can run the simulations by yourself, just use the lower part of this page.



This page is a response to the kind request of Joel Dietz, the creator of metalambda.org, for his metaseminar 0 (link to be updated if transcript available).