Fold rewrite, dynamic DNA material and visual DSD

As it happened with chemlambda programs, I decided it is shorter to take a look myself at possible physical realizations of chemlambda than to wait for others, uninterested or very interested really, people.

Let me recall a banner I used two years ago[Knitting-Crown]-Keep-Calm-And-Use-Rna-For-Interaction-Nets

It turns out that I know exactly how to do this. I contacted Andrew Phillips, in charge with Microsoft’ Visual DSD  with the message:

Dear Andrew,

I am interested in using Visual DSD to implement several graph-rewriting formalisms with strand graphs: Lafont Interaction Combinators, knots, spin braids and links rewrite systems, my chemlambda and emergent algebra formalisms.

AFAIK this has not been tried. Is this true? I suggest this in my project chemlambda but I don’t have the chemical expertise.

About me: geometer working with graph rewrite systems, homepage: or

Some links (thank you for a short reception of the message reply):

– github project:
– page with more links:
– arXiv version of my Molecular computers article

Emergent algebras:
– em-convex


I still wait for an answer, even if Microsoft’ Washington Microsoft Azure and Google Europe immediately loaded the pages I suggested in the mail.

Previously, I was noticed by somebody [if you want to be acknowledged then send me a message and I’ll update this] about Hamada and Luo Dynamic DNA material with emergent locomotion behavior powered by artificial metabolism  and I sent them the following message

Dear Professors Hamada and Luo,

I was notified about your excellent article Dynamic DNA material with emergent locomotion behavior powered by artificial metabolism, by colleagues familiar with my artificial chemistry chemlambda.

This message is to make you aware of it. I am a mathematician working with artificial chemistries and I look for ways to implement them in real chemistry. The shortest description of chemlambda is: an artificial chemistry where the chemical reactions are alike a Turing complete family of graph rewrites.

If such a way is possible then molecular computers would be not far away.

Here is a list of references about chemlambda:

– GitHub repository with the scripts
– page which collects most of the resources

Thank you for letting me know if this has any relation to your interests. For my part I would be very thrilled if so.

Best regards,
Marius Buliga

Again, seems that these biology/chemistry people have problems with replies to mathematicians, but all ths makes me more happy because soon I’ll probably release instructions about how everybody could make molecular computers along the lines of Molecular computers.

I’ll let you know if there are future “inspiration” work. Unrelated to chemlambda, there are several academic works which shamelessly borrow from my open work without acknowledgements, I’ll let you know about these and I’ll react in more formal ways. I hope though this will not be the case with chemlambda, however, this happened before twice at least.  (I say nothing about enzymes/catalysts, category theory and cryptocurrencies… for the moment.)

Finally, here is a realization of the lambda calculus beta rewrite via a FOLD rewrite


which shares a relation with the ZIP rewrite from Zipper Logic. It seems I was close to reality,  now though I got it exactly 🙂 .

Let’s talk soon!




Small graph rewrite systems (5)

Here are some more tentative descriptions of system X and a play with the trefoil knot. This post comes after the intermezzo and continues the series on small graph rewrite systems.

Recall that system X is a proposal to decompose a crossing into two trivalent nodes, which transforms a knot diagram into an unoriented stick-and-ring graph.


The rewrites are the following, written both with the conventions from the stick-and-ring graphs and also with the more usual conventions which resemble the slide equivalence or spin braids mentioned at the intermezzo.

The first rewrite is GL (glue), which is a Reidemeister 1 rewrite in only one direction.


The second rewrite is RD2, which is a Reidemeister 2 rewrite in one direction.


There is a DIST rewrite, the kind you encounter in interaction combinators or in chemlambda.


And finally there are two SH rewrites, the patterns as in chemlambda or appearing in the semantics of interaction combinators.



One Reidemeister 3 rewrite appears from these ones, as explaned in the following figure (taken from the system X page).


Let’s play with the trefoil knot now. The conversion to stick-and rings


is practically the Gauss code. But when we apply some sequences of rewrites


we obtain more complex graphs, where

  • either we can reverse some pairs of half-crossings into crossings, thus we obtain knotted Gauss codes (?!)
  • or we remark that we get fast out of the Gauss codes graphs…

thus we get sort of a recursive Gauss codes.

Finally, remark that any knot diagram has a ring into it. Recall that lambda terms translated to chemlambda don’t have rings.

An example of “Official EU Agencies Falsely Report More Than 550 URLs as Terrorist Content”

Today I read Official EU Agencies Falsely Report More Than 550 URLs as Terrorist Content.  Two comments on this.

1. It happened to me in Feb 2019. I archived one of my stories from the chemical sneakernet universe. The original story is posted on Here is the message which appeared when I checked the archived link:


What? I contacted and got an answer from the webmaster, pretty fast. The problem was with, not with my link in particular. Now the archived link is available.

After I sent the message to archive but before I received the answer, I searched for a way to contact EU IRU, to ask what the problem might be.  I was unable to identify any such way. However there was a way to send a message to EU officials, who might redirect my message to whom it may concern. It worked, but it took longer than the time needed by archive webmaster to respond and unblock the link. I was not contacted since.

2. As you see in the post from archive, it was not EU IRU the institution which sent the blocking orders. But nevermind, how can one try to block arXiv articles? This reminded me of a very recent story: Google Scholar lost my Molecular computers arXiv article. As the article is on the same subject as the story from point 1, I wonder if by any (mis)chance Google Scholar received a blocking order.

System X, semantic pain and disturbing news to some

This is a temporary post. Soon some news will come, some disturbing for some. This is just to entertain you with the System X, a small graph rewrite system proposed as a replacement for slide equivalence. Here is some prose I wrote while trying to understand 3 tiny graphic beta rewrites. This qualifies as semantic pain, but it was a very good exercice because it gives ideas (to those prone to have them, as opposed to those who lack personal ideas and take them without acknowledgement).

Small graph rewrite systems (4)

This post follows Problems with slide equivalence. A solution is to replace slide equivalence with System X.

This supposes to change the decomposition of a crossing like this:


I let you discover system X (or will update later) but here I want to show you that the Reidemeister 3 rewrite looks like that:


There is now a page dedicated to small graph rewrite systems and stick-and-rings graphs.


Google Scholar lost my molecular computers

Today I noticed that my Molecular computers article arXiv:1811.04960 is replaced by Google Scholar with the unrelated article  Defining Big Data Analytics Benchmarks for Next Generation Supercomputers, arXiv:1811.02287. I’m not an author of that article.

Screenshot from 2019-04-07 21:52:00


A cosmic ray is the cause?

Google search can still find it, but Google Scholar gives the wrong result.

UPDATE: I added the article by hand, but the link to the source (i.e. arXiv article) is not present. How can they loose arXiv articles? Or more precisely  arXiv e-prints , in no place arXiv uses the name “preprint arXiv”. Maybe google scholar merged with legacy publishers, who knows, these days…

Do you experience errors in Google Scholar?

Problems with slide equivalence

UPDATE: System X is a solution.


After the Intermezzo, in this post I’ll concentrate on the slide equivalence for unoriented (virtual) links, as defined in L.H. Kauffman, Knots and Physics, World Scientific 1991, p. 336.



Later on we shall propose a small graph rewrite system which is different from this, but we first need to understand that there are some problems with slide equivalence.

Kauffman rule I’ is half a definition, half a rewrite rule. He gives two decompositions of a crossing into two 3-valent nodes. The rewrite is that we can pass from one decomposition to the other.

Problem 1. How many types of 3-valent nodes are used? My guess is just one.


Problem 2. Is the rule II’ needed at all? Why not use instead the rule III’, with the price of a loop:


Problem 3. Is the rule I’ too strong? Maybe, look at the following configuration made of two crossings.


Neighboring crossings dissappear.

We don’t even need two neighboring crossings. In the next figure I took the left pattern from the rule IV’, first part. It is also a pattern where the rules I’, then III’ apply.


The result is very different from the application of IV’.

The same happens for the right pattern of the rule IV’, first part.


We can use again I’ and III’ to obtain a very different configuration than expected.


Conclusion.  The slide equivalence rewrites with a “dumb” algorithm of rewrites application behaves otherwise than expected. By “dumb” I mean my favorite algorithms, like greedy deterministic or random.

Used with intelligence, the slide equivalence rewrites have interesting computational aspects, but what about the “intelligent” algorithm? Kauffman brains are rare.



computing with space | open notebook

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