Tag Archives: walking machine

Walker eating bits and a comment on the social side of research

This post has two parts: the first part presents an experiment and the second part is a comment on the social side of research today.

Part 1: walker eating bits.  In this post I introduced the walker, which has been also mentioned in the previous post.

I made several experiments with the walker, I shall start by describing the most recent one, and then I shall recall (i.e. links to posts and vids) the ones before.

I use the chemlambda gui which is available for download from here.

What I did: first I took the walker and made it walk on a trail which is generated on the fly by a pair A-FOE of nodes. I knew previously that such a pair A-FOE generates a trail of A and FO nodes, because this is the basic behaviour of the Y combinator in chemlambda. See the illustration of this (but in an older version, which uses only one type of fanout nodes, the FO) here.  Part of it was described in the pen-and-paper version in the ALIFE14 article with Louis Kauffman.

OK, if you want to see how the walker walks on the trail then you have to download first the gui and then use the gui with the file walker.mol.

Then I modified the experiment in order to feed the walker with a bit.

A bit is a pair of A-FO nodes, which has the property that it is a propagator. See here the illustration of this fact.

For this I had to modify the mol file, which I did. The new mol file is walker_eating_bit.mol .

The purpose of the experiment is to see what happens when the walker is fed with a bit. Will it preserve its shape and spill out a residue on the trail? Or will it change and degenerate to a molecule which is no longer able to walk?

The answer is shown in the following two screenshots. The first one presents the initial molecule described by the walker_eating_bit.mol.

At the extreme right you see the pair A-FOE which is generating the trail (A is the green big node with two smaller yellow ones and a small blue one and the FOE is the big yellow node with two smaller blue ones and a small yellow one). If you feel lost in the notation, then look a bit at the description in the visual tutorial.

In the middle you see the walker molecule. At the right there is the end of the trail. The walker walks from left to right, but because the trail is generated from right to left, this is seen as if the walker stays in place and the trail at its left gets longer and longer.

OK. Now, I added the bit, I said. The bit is that other pair of two green nodes, at the right of the figure, immediately at the left of the A-FOE pair from the extreme right.

The walker is going to eat this pair. What happens?

I spare you the details and I show you the result of 8 reduction steps in the next figure.


You see that the walker already passed over the bit, processed it and spat it as a pair A-FOE. Then the walker continued to walk some more steps, keeping its initial shape.

GREAT! The walker has a metabolism.

Previous experiments.  If you take the walker on the trail and you glue the ends of the trail then you get a walker tchoo-tchoo going on a circular trail. But wait, due to symmetries, this looks as a molecule which stays the same after each reduction step. Meaning this is a chemlambda quine. I called such a quine an ouroboros. In the post Quines in chemlambda you see such an ouroboros obtained from a walker which walk on a circular train track  made of only one pair.

I previously fed the walker with a node L and a termination node T, see this post for pen and paper description and this video for a more visual description, where the train track is made circular as described previously.

That’s it with the first part.

Part 2: the telling silence of the expert. The expert is no lamb in academia. He or she fiercely protect the small field of expertise where is king or queen. As you know if you read this open notebook, I have the habit of changing the research fields from time to time. This time, I entered into the the radar of artificial chemistry and graph rewriting systems, with an interest in computation. Naturally I tried to consult as many as possible experts in these fields. Here is the one and only contribution from the category theory church.  Yes, simply having a better theory does not trump racism and turf protection.  But fortunately not everything can be solved by good PR only. As it becomes more and more clear, the effect of promotion of mediocrity in academia, which was consistently followed  since the ’70, has devastating effects on the academia itself. Now we have become producers of standardised units of research, and the rest is just the monkey business about who’s on top. Gone is the the trust in science, gone are the funds, but hey, for some the establishment will still provide a good retirement.

The positive side of this big story, where I only offer concrete, punctual examples, is that the avalanche which was facilitated by the open science movement (due to the existence of the net) will change forever the academia in particular. Not into a perfect realm, because there are no such items in the real world catalogue. But the production of scientific research in the old ways of churches and you scratch my back and I’ll scratch yours is now exposed to more eyes than before and soon enough we shall witness a phenomenon similar to the one happened more than 100 years ago in art, where ossified academic art sunk into oblivion and an explosion of creativity ensued, simply because of the exposure of academic painting along with alternative (and, mixed with garbage, much more creative artists) works in the historical impressionist revolution.



Ouroboros predecessor (IV): how the walker eats

Continues from  Ouroboros predecessor (III): the walking machine .  This time you have to imagine that the walker machine sits on a long enough train track.

The regularity of the train track is corrupted by a bit of food (appearing as a L node connected to a termination node), see the next (BIG) picture. It is at the right of the walker.

You can see (maybe if you click on the image to make it bigger) that the walker ingests the food. The ingested part travels through the walker organism and eventually is expelled as a pair L and A nodes.




Perhaps, by clever modifications of the walker (and some experiments with its food) one can make a Turing machine.

This would give a direct proof that chemlambda with the  sequential strategy is universal as well. (Well, that’s only of academic interest, to build trust as well, before going to the really nice part, i.e. distrbuted, decentralized, alife computations.)


Ouroboros predecessor (III): the walking machine

In the post   Ouroboros predecessor (II): start of the healing process   there is a curious phenomenon happening: there are 3 quasi-identical reduction steps, each involving 8 reductions.

That is because there is a walking machine in those graphs.

Explanations follow.

Recall the reduction strategy:

  • at each step we do all the possible (non-conflicting) graph rewrites involving the moves BETA, FAN-IN, DIST, LOC PRUNING, from left to right only. See the  definition of moves post.
  • then we do all the COMB moves until there is no COMB move possible (also from left to right only).
  • then we repeat.

In the drawings the COMB moves are not figured explicitly.

Let’s come back to the walking machine. You can see it in the following figure.



In the upper side of the figure we see one of the graphs from the reduction of the “ouroboros predecessor”, taken fom the last post.

In the lower side there is a part of this graph which contains the walking machine, with the same port names as in the upper side graph.

What I claim is that in a single reduction step the machine “goes to the right” on the train track made by pairs of FO and A nodes. That is why some of the reduction steps from the last post look alike.

One reduction step will involve:

  • 8 reduction moves, namely 4 DIST, 2 BETA, 2 FAN-IN
  • followed by some COMB moves.

Let’s start afresh, with the walking machine on tracks, with new port names (numbers).



For the sake of explanations only, I shall do first the two BETA and the two FAN-IN moves, then will follow the four  DIST moves. There is nothing restrictive here, because the moves are all independent, moreover, according to the reduction strategy, these are all the moves which can be done in this step, and they can be done at once.

OK, what do we see? In the upper side of this figure there is the walking machine on tracks, with a new numbering of ports. We notice some patterns:

  • the pair of L and A nodes, i.e. L[1,2,3] A[2,35,1]  which, in the figure, appears over the A node  A[3,4,5]. Remark that A[3,4,5] would make a good pair (i.e. a part of the “track”) with FO[38,4,36], if it would have the ports  “3” and “5”  switched.
  • the pattern of 5 red FI and L nodes from the middle upper side of the walking machine
  • the 3 green and 2 red nodes which make a kind of a pentagon at the right side of the walking machine
  • the 2 DIST right patterns for application node (green) and the 2 DIST right patterns for the lambda node (3 red, one green) which are like 4 train cars on the track.

In the lower part of the figure we see what the graph looks like after the application of the 2 BETA moves and the 2 FAN-IN moves which are possible.

Let’s look closer. In the next figure is taken the graph from the lower part of the previous figure. Beneath it is the same graph, only arranged on the page such that it becomes simpler to see the patterns. Here is this figure:




Recall that we are working with graphs (called g-patterns, or molecules), not with particular embeddings of the graphs in the plane. The two graphs are the same, only the drawings on the plane are different. Chemlambda does not matter about, nor uses embeddings. This is only for you, the reader, to help you see things better.

OK, what do we see:

  • there are some arrows (edges) with 2 names on them, this is because there are Arrow elements which still exist because we have not done yet the COMB moves
  • we see that already there is a new pair of A and FO nodes (in green, at the left of the lower graph). At the right of the lower graph we see that there is a missing piece of train track which “magically” appeared at the left.
  • then, at the right of the piece of the train track piece which appeared at left, the walking machine already looks like before the moves, in the sense that there is an A node  with “switched” ports, there is a pair of green and red nodes hovering over it,
  • moreover the pattern of 5 red nodes is there again, …

… but all these patterns are not the old ones, but new ones!

The 4 train cars made by DIST patterns are missing! Well, they appear again after we do the remaining 4 DIST moves.

In the next figure we see the result of these 4 DIST moves. I did not numbered the new edges which appear.




I also did the COMB moves, if you look closer you will see that now any arrow either has one or no number on it. The arrows without numbers are those appeared after the DIST moves.

Let’s compare the initial and final graphs, in the next figure.




We see that indeed, the walking machine went to the right! It did not move, but instead the walking machine dismembered itself and reconstructed itself again.

This is of course like the guns from the Game of Life, but with a big difference: here there is no external grid!

Moreover, the machine destroyed 8 nodes and 16 arrows (by the BETA, FAN-IN and COMB moves) and reconstructed 8 nodes and 16 arrows by the DIST moves. But look, the old arrows and nodes migrated inside and outside of the machine, assembling in the same patterns.

This is like a metabolism…