Talk:Von Neumann universal constructor

Citation

He observed that -

This citation is probably best derived from the writing contained within the text due Jeffress, Cerebral Mechanisms in Behavior - The Hixon Symposium: pages 30-31 contain the text "typical traits which appear in connection with mutation, leathally as a rule, but with a possibility of continuing reproduction with a modification of traits." Clearly, the italicised portion of this quote is a satisfactory definition for the term open-ended evolution. William R. Buckley 20:17, 11 March 2007 (UTC)

Nobili-Pesavento 29-state

What is this? Is this a turing-machine in a celular automata? Could someone explain this further? 84.59.213.173 (talk) 01:34, 31 January 2008 (UTC)

It is not a TM in a CA. Rather, it is supposed to be a UC in a CA. In point of fact, it is a capable constructor, though not a UC. It is also not a self-replicator. For more information, see Nobili's website: http://www.pd.infn.it/~rnobili/ William R. Buckley (talk) 19:28, 1 March 2008 (UTC)

You might also review the proceedings for Automata 2008, which is searchable on Amazon. William R. Buckley (talk) 23:23, 16 June 2008 (UTC)

Merging

These two articles ought to be merged because they both discuss the same subject matter. —Preceding unsigned comment added by Maverick1701 (talk • contribs) 17:42, 1 March 2008 (UTC)

Thes two articles should not be merged, and for the same reason as not merging with the *Self-replicating machine* article. Universal assembler is one case, while the von Neumann universal constructor is another case. Further the vN UC is like the Turing TM (both abstract, formal concepts), while the universal assembler (however vaguely described) is expectedly a real (physical) device. William R. Buckley (talk) 19:09, 1 March 2008 (UTC)

As no further discussion has been observed, I am removing the flag. William R. Buckley (talk) 17:48, 26 May 2008 (UTC)

Pesavento's design

In the proceedings volume for the conference Automata 2008, which is searchable on Amazon at the URL

http://www.amazon.com/Automata-2008-Theory-Applications-Cellular-Automata/dp/1905986165/ref=sr_1_1?ie=UTF8&s=books&qid=1211820017&sr=8-1, see page 501

the topic of von Neumann self-replicators is discussed. One of the conclusions presented in the paper is the fact of insufficiency, vis-à-vis self-replication, of the Pesavento design, as presented in the journal Artificial Life. The point is that one cell of the configuration cannot be constructed by the configuration, and so it is not a self-replicator. It would seem to me that use of the Pesavento design as an example self-replicator is to the detriment of Wikipedia. William R. Buckley (talk) 16:52, 26 May 2008 (UTC)

I think you are wrong. The 32-state Nobili-Pesavento machine (as presented in the 1994 Pesavento ALife article, distributed as tape.evn with the 1994 source code, and as SR_CBC_AP_OLD.EVN with Nobili's WJVN package) is perfectly capable of unlimited repeated replication, given a suitable tape. See [1] Ferkel (talk) 17:10, 1 August 2008 (UTC)

Well then, Dr. Hutton, the challenge is thus extended to you - demonstrate so, without adding any configuration to the Pesavento design. A suitable simulator is now available. Prove your point. William R. Buckley (talk) 18:56, 1 August 2008 (UTC)

Also, your assertion of performance by the Pesavento corpus is a very poor second to the demonstration I gave you. William R. Buckley (talk) 19:16, 1 August 2008 (UTC)

Here: [2] Ferkel (talk) 09:26, 4 August 2008 (UTC)

Found a few errors. One is in the tape construction python script for the Pesavento design - the tape is placed incorrectly versus the configuration. Also, construction occurs one row above the location it should, and so the tape replicant is placed incorrectly versus the corpus replicant. Also, the placement of the return signal path from the read/write head makes no sense - a downward pointing ordinary transmission state, instead of one pointing to the left. Bottom line - your demonstration proves my point. William R. Buckley (talk) 06:23, 5 August 2008 (UTC)

Assuming various corrections, I can concede Pesavento's configuration does indeed self-replicate. If it had needed to use any additional configuration, I would not have agreed it is a self-replicator. This in no way addresses the issue of inapplicability to von Neumann's problem. And, just in case you care, von Neumann addressed the issue of special signal crossing states. The reference is in Automata 2008. Interesting that the command to extend the construction arm is useful to circumvent an otherwise troublesome matter. How did you come by it? William R. Buckley (talk) 07:12, 5 August 2008 (UTC)

For those less familiar with the details of Pesavento's design, it will be appreciated that generally, one does not expect that collisions between a construction arm and the cells to which it writes will be predictable. The general expectation is that construction signal should be delivered exclusively to cells in the ground state. In the case of my complaint regarding the claim of self-replicability, it was that a cell is unavailable to the construction arm. The solution turns on use of the signal to extend the construction arm as a mechanism of destruction, thus removing the cells of the tape which prevent this construction arm access. It is, for me at least, an unexpected benefit; just the right signal, in just the right circumstance.

My expectation was that the Pesavento design would need to construct an external mechanism, which when triggered would construct this claimed unavailable cell, yielding a different design; i.e. not the one published.

While I stand corrected on the self-replicability claim, I will yet hold to one important concern regarding this mechanism: Given its importance to solve an otherwise difficult aspect of constructing this cell in question (just above the left-most cell of the tape), why is there no mention of the mechanism in the Pesavento paper? Also, it is a Nobili Cellular Automaton, not a von Neumann Cellular Automaton. William R. Buckley (talk) 18:38, 5 August 2008 (UTC)

Re errors/corrections: I think you were running the script on tape.evn or similar, not SR_CBC_AP_OLD.EVN as per the instructions. These files contain the same replicator but with some tiny differences - tape.evn has the activation line vertical, SR_CBC_AP_OLD.EVN has an error in the C-arm head. Of course the script can easily be adapted to work with tape.evn instead.

Re the C-arm transcription error manoeuvre: This can be seen in SR_CBC_AP_OLD.EVN, where by coincidence the transcription error is circumvented by the tape provided: first advancing by 2 then moving up. Nobili's superb C-ARM_CONTROLS.EVN allowed me to test this manoeuvre and also the solution to the tape-inset issue. Both minor issues, in the end.

Re the applicability to von Neumann's problem and the 32-state rules: I think you're wrong about this. See the McMullin paper [3]. The paper suggests that the problem von Neumann was trying to solve concerned how a self-reproducing machine could undergo inheritable mutations and grow in complexity. JvN sketched a solution in a 29-state CA but never completed it. Nobili and Pesavento gave the first fully-implemented solution, in a slightly extended 32-state CA. (I've put a demonstration of inheritable mutations here: [4] that I hope illustrates the point McMullin was making.) As McMullin says "... Because these three systems [Thatcher, Codd, Pesavento] are so very closely related to von Neumann's it follows that they are at least equally satisfactory in solving his problem." If you think the Wikipedia article should present a different view to this then by the No Original Research rule WP:NOR we'll need to find citations that support this view, and then we can 'present the controversy'. (And not your papers, see WP:COI and WP:COS.)

Either way, the von Neumann UC article needs a clean-up, to retract your claim that the Nobili-Pesavento 32-state implementation isn't a self-replicator, and also to show the new self-rep screenshots that Golly can give us. We can remove the Nobili-Pesavento 29-state design, if you like, since as you have pointed out this is not a self-replicator. Did they ever claim this in any of their papers...? Ferkel (talk) 20:52, 6 August 2008 (UTC)

I've given you the citation, and to work of von Neumann, which you have continued to ignore, and which addresses exactly this issue. See my paper for the proper reference in von Neumann's posthumous book; page 191. William R. Buckley (talk) 03:08, 7 August 2008 (UTC)

I have no problem with Dr. McMullin's point; the three solutions are reasonably applied to the same problem. That in no way alters my position on the propriety of calling NP32 a von Neumann self-replicating cellular automaton; and I quote from von Neumann:

"For this reason we accept the subordinate difficulty of line-crossing in 2 dimensions and the necessity of special constructions to overcome it." This comes from page 191, near the bottom of the page, of von Neumann's Theory of Self-Reproducing Automata. See the URL http://www.walenz.org/vonNeumann/page0209.html

Thus, von Neumann specifically excluded the possibility of using a dedicated state as means to solve the signal crossing (line-crossing) problem; he was satisfied that all signal crossing needs could be accommodated with the existing 29 states. The 32 state system is not von Neumann; it is Nobili. NCA and vNCA are analogs of each other; they do not comprise an identity, any more than do the rules of von Neumann versus those of Codd, or of Conway for that matter. That differing tools may be applied to a common problem does not make those tools identical.

Regarding listing NP32 as a self-replicator, clearly I do not complain given demonstration. This will naturally extend to suggestions that NP32 provides a very good approximation of the von Neumann equivalent; the systems are inter-convertible, as I have shown. William R. Buckley (talk) 04:29, 7 August 2008 (UTC)

As to any claim that NP29 is a self-replicator, no, I don't believe any such claim was made. Regarding NP32, I have tried in the past to get Pesavento to discuss the self-replication process, and to no avail. I imagine that you spent a good deal of time searching for the antidote to my concerns regarding NP32 self-replicability. William R. Buckley (talk) 04:35, 7 August 2008 (UTC)

I did indeed use a rendition of NP32 which I had obtained from Nobili some time ago (circa 2003), well before he compiled, much less released, his distribution. So, I did also have to make a few adjustments; wasn't aware of the variations between distributions; admittedly, some of mine were private. William R. Buckley (talk) 04:44, 7 August 2008 (UTC)

I should add some commentary regarding the differences between the work of Thatcher, and the works of Codd and Pesavento. Thatcher's was in the 29-state system; the other two were not. Thus, Thatcher's work is directly applicable to von Neumann's problem - signal crossing in 29 states; the other two are not. William R. Buckley (talk) 05:05, 7 August 2008 (UTC)

There are two von Neumann problems, then. One concerns open-ended evolution, and the other signal crossing mechanisms. I draw the line at different mechanisms with different regime problems, all being applied to another problem. Pesavento is not a von Neumann cellular automaton but, it expectantly is an open ended evolver. William R. Buckley (talk) 18:10, 7 August 2008 (UTC)

PNGs

Ferkel: Is there no means to obtain better quality images; something that shows individual cells sufficient to determine state? William R. Buckley (talk) 03:37, 16 August 2008 (UTC)

More on Pesavento

In your work on Pesavento, has it occurred to you that other, quite simple means exist to both render the design a self-replicator, and without need to rely upon collision of the construction arm with tape as a means to avoid the otherwise troublesome matter of constructing a certain cell? Indeed, all one need do is to extend by quite some time the delay observed by the auto-retract signal, such that it is serviced after service of the corresponding construction signal; alter the visitation order of these signals upon the construction arm, and the problem disappears. I think this is more elegant a mechanism, than is the mechanism which the Pesavento design employs. William R. Buckley (talk) 03:48, 16 August 2008 (UTC)

Mange: JvN Consistent Configuration

It should be noted that the reasoning for the declaration in Mange et al. is that the configuration there mentioned as being *consistent with the design of von Neumann* is so judged because it uses only the 29-states of von Neumann. William R. Buckley (talk) 04:44, 16 August 2008 (UTC)

This is to say, I do not expect that Mange et al. were intent to claim the architecture of the design is even minimally identical to that contemplated by von Neumann. Indeed, architecturally they are not at all related, even though we might forget for the moment that von Neumann's architecture is only half complete; half the details are missing. William R. Buckley (talk) 13:08, 9 September 2008 (UTC)

Implementation

Declaring NP32 the first universal constructor is perhaps going a bit too far, though it may require a bit of clever wording to correct. My complaint is that NP32 is the first implemented UC for a CA. It may be that other programs have expressed universal construction, though the fact is not recognised. I am thinking of compilers, and viruses, etc. William R. Buckley (talk) 04:52, 16 August 2008 (UTC)

Simple Definition

It will require great care to properly handle the misconceptions implied by the simple definition of universal construction. Part of the reason is that no vNCA Garden of Eden configuration is passive. The best analogy comes from Douglas Hofstadter, who in Godel, Escher, and Bach: An Eternal Golden Braid mentions the phonograph player, which cannot play all possible phonographs: at least some of those phonographs will cause the player to break (think of standing waves in the player, whose energy increases by constructive interference with the waves emitted by the phonograph upon scratching it with a needle); there is no phonograph player that can play all possible phonographs. Similarly, there is no universal constructor; all constructors are limited in their ability to construct, and this includes configurations which are not GoE's. The key element in constructibility is the presence and nature of signal which is external to the constructor. William R. Buckley (talk) 18:10, 17 August 2008 (UTC)

Of course, the better definition is like that which applies to the mechanism of computation: a UC (UTM) can construct (compute) any constructible (computable) construction (computation) that can be constructed (computed). William R. Buckley (talk) 08:07, 21 August 2008 (UTC)

evolution

there are some assertions that VN's machine guarantees the possibility of mutation and evolution by natural selection. this seems like a pretty silly claim ... although a replicator with a changeable information component is necessary for evolution, it seems quite reasonable to suppose you can have a brittle self-replicator that won't function with any changes. The important fact seems to be that VN has proved the possibility of self-replicators at all, and the dubious assertion that this is a robust replicator capable of evolution, while interesting, seems to detract from the important point rather than improve the article. comments? 131.172.99.15 (talk) 03:02, 21 August 2008 (UTC)snaxalotl

I mention this earlier on this Talk page, under the title Citation. Von Neumann himself gave the argument, noting that arbitrary mutation would likely be lethal but that there was also a chance for evolutionary change; see the quote above. (I argue that upon this expectation alone, von Neumann would have rejected any configuration which does not fulfill the behaviors of tape replication, configuration construction, controlled relative placement of these, starting of the construct, and a return to initial conditions - or some other means of repetitive replication; anything less is not a self-replicator - at best, just a constructor). He tended to confine that change to the tape, the obvious means to heritability. This does not imply that von Neumann excluded consideration of other mutation, such as that which might occur during construction of the daughter configuration, as opposed to the daughter tape. The brittleness of one instantiation says nothing about other instantiations; there likely exist computational models which are not brittle; the classic complaint is that vNCA are brittle. The proof of self-replicators is visible for all to see: biological organisms; machine self-replication follows directly. What von Neumann did was show how to build such machines, by denoting both the logical requirements, and a set of suitable parts; indeed, for parts he did this twice (kinematic and tesselation), and toyed (TinkerToys, actually) with a third. I agree most with your mention of the environment; the locus of the constructor. However, that some construction occurs by interaction with the environment in no way implies that living systems (open-ended evolvers) cannot thereupon exist. William R. Buckley (talk) 04:00, 21 August 2008 (UTC)

The implied minority of viable mutations falsifies the absolute negative in the last sentence. I'll try to find a cite-able reference to support my objection, then I'll include that. Voland0 (talk) 00:49, 19 October 2018 (UTC)

VN (see page 85 and beyond of fifth lecture in Theory of Self-Reproducing Automata), very clearly talks about evolution that can be robust in his conceptual scheme. This is done by introducing an Automaton D which is not involved in the basic function of self-replication and whose function does not disturb the basic performance of the universal constructor (A) + universal copier (B) + operating system (C). If there is a mutation in the D part of the description, say D`, then the system (A + B + C + D) + Φ(A + B + C + D`) will produce (A + B + C + D`) + Φ(A + B + C + D`). VN further proposed that non-trivial self-reproduction should include this “ability to undergo inheritable mutations as well as the ability to make another organism like the original”, to distinguish it from “naive” self-reproduction like growing crystals. So the basic self-replication scheme (A + B + C) + Φ(A + B + C) should be unaffected by D, which can be seen as the extra functioning of an organism's phenotype---all the things that make it more or less fit and thus selected for. See references in text for Brenner and Rocha. I added materials to help make this more clear in article. --PlaceboOracle (talk) 18:38, 14 May 2020 (UTC)

Configuration Size

It is interesting that while the concept of configuration size minimisation is discussed, especially considering the emphasis given Run-Length Limited encoding, yet it seems that such mechanisms do not yield the smallest configurations, nor the shortest tapes. NCA configurations having 3343 cells, a tape of 44,150 cells, for 8830 5-bit instructions, and 3574 cells in the configuration, 37,780 cells in the tape, for 9445 4-bit instructions are known. William R. Buckley (talk) 05:54, 15 September 2008 (UTC)

Article Misrepresentations as of 20081115

It is incorrect to call the NP29 configuration a universal constructor. Indeed, none of the published *self-replicators* for vNCA (29 states)and NCA (32 states) is a universal constructor. Not one of them can construct, for instance, the Real-Time Crossing Organ, as given by Gorman. Properly, these configurations are all general constructors; they may construct any passive configuration.

Not only have I given two vNCA configurations which are self-replicators, I have also given a total of four NCA configurations which are also self-replicators; one of the latter is the quickest self-replicator for NCA, which has both nearly smallest corpus (a sister configuration is about 100 - 200 cells smaller) and the shortest tape yet given. Use of Golly will quickly reveal the two flathead designs. I am still waiting for a reply from Nobili, as to whether or not he can give a smaller configuration, or a shorter tape; one expects that time to self-replication is dependent upon these two parameters.

On this point, neither of the vNCA configurations are the partial constructor. In truth, I have published three vNCA self-replicators; two are holistic, and one is a partial constructor. William R. Buckley (talk) 19:01, 19 February 2009 (UTC)

One final note. In all of this work, there has been a tacit acceptance of von Neumann's assertion that self-replication is but a special case of universal construction. This is not correct, in my view. Indeed, one can demonstrate that self-replication is not possible given possession of a universal constructor (universal over passive configurations). To see this, review the paper Computational Ontogeny, Biological Theory, Vol 3 No 1. I state here the intention to demonstrate same. I will do it with the partial constructor; this is the configuration mentioned by Mange. William R. Buckley (talk) 05:33, 16 November 2008 (UTC)

As to the correctness of dates of publication, the partial constructor is the product of my graduate work, and was completed in December, 1999, when I submitted the corresponding documentation (a mix of thesis and project) in consideration of the award of master of science in computer science, January, 2000. Hence, it is incorrect for other editors of this Wikipedia article to assert by text therein that Renato Nobili's works demonstrate a return to initial condition prior to such demonstration by my works; a minor point, but incorrect. William R. Buckley (talk) 19:01, 19 February 2009 (UTC)

The two flathead designs given with the Golly 2.0 distribution are two of a set of three NCA self-replicators. These three designs are at a sweetspot of the intersection between data and process (something that would be investigate-able were an algebra of algorithms available). The simplest design has the smallest configuration size, and the longest tape. The most complex design has the smallest tape, the largest configuration size, and the shortest time to self-replication. All the configurations are of size less than 4000 cells, sans tape. William R. Buckley (talk) 19:01, 19 February 2009 (UTC)

Excised Detail - Capabilities of NP29 Configuration

I excised this phrase "and its offspring are not self-replicable" because it is ambiguous.

One may construct a tape of the 29-state configuration, and then the statement makes sense.

Except in the following case. It is possible to construct a description (D) for machine A, which includes a description of the tape which machine A needs in order to self-replicate. In that case, construction from D does not constitute self-replication. This is true even if machine A is the machine which constructs according to the instructions in D. Here, the offspring may well be self-replicable, even if their construction does not constitute an act of self-replication. The reason is that machines derived from D will inherit tape A, not tape D.

The words *offspring* *daughter* and *construct* are synonyms for the product of construction. I would suggest that the phrase is better expressed as "and its replicants are not self-replicable" to distinguish the nature of the construct - does it describe the machine which interprets the tape, or a machine other than the one which interprets the tape (which would be a construct).

The language for this distinction in cellular automata is not well developed. William R. Buckley (talk) 23:13, 22 August 2009 (UTC)

Clarification needed

From my vague memories of a class in Artificial Life I took almost a decade ago, I understood this construction of von Neumann to be an attempt to produce a self-replicating Turing machine; this article appears to support that view. Could the wiki article detail how accurate that description is, i.e. how well did von Neumann fare in his attempt? Pcap ping 23:12, 1 September 2009 (UTC)

If you look at the last theorem in that article (Smith, 1968), it's clearly possible to have a CA that is self-reproducing and computes any μ-recursive function, i.e. equivalent to a Turing machine. I've not read the article closely enough to tell if that is possible using von Neumann's construction or if substantial modifications are required. But this wiki article needs updating as it's missing a major aspect from the discussion. Pcap ping 23:24, 1 September 2009 (UTC)

I will argue that Arbib is wrong, if indeed he states that von Neumann was interested in modeling a Turing machine. It is clearly the case that von Neumann's cellular automata are capable of representing a Turing machine. However, and this point is mentioned by von Neumann in Hixon, the Turing machine was simply a point of reference, a hint as to the nature of a machine which is capable of self-replication. The important point is not computation, but construction. Von Neumann modeled his notion of universal construction upon Turing's notion of universal computation. In my view, no further claim should be made. William R. Buckley (talk) 11:26, 24 November 2009 (UTC)

Traditional View

It is not exactly true to state that the traditional view of von Neumann's work in machine self-replication is that of the logical requirements for same. Indeed, it is generally understood that Hixon addressed the logical requirements for non-trivial self-replication. The opening paragraph of the section Purpose is therefore poorly constructed; Codd retained this orientation (as I recall, it is explicitly stated in his doctoral thesis), and the works of later researchers (such as Langton) were intended to address the minimisation of configuration, and simplification of underlying cellular automata, with the concomitant retention of non-triviality. After all, one can go all the way to Ulam to see that self-replication is trivially achieved in some systems. William R. Buckley (talk) 11:18, 24 November 2009 (UTC)

time-steps for replication references

Where do the numbers in the Table - Comparison of implementations - and in particular the number of time-steps for different implementations come from? Are there any peer-reviewed publications associated with these? The publications of Pesavento and Nobili that are linked from the article do not discuss practical implementations from what I can see.

Alvis Brazma (brazma@ebi.ac.uk) — Preceding unsigned comment added by 193.62.194.241 (talk) 10:33, 7 October 2013 (UTC)

Downloads

Can somebody provide a download for phi9.rle and codon3.rle? 76.232.22.106 (talk) 18:43, 8 July 2018 (UTC)

Universal computer-constructor

Forum etc. —DIYeditor (talk) 17:15, 28 August 2018 (UTC)
The following discussion has been closed. Please do not modify it.
I am constructing a machine that is capable of constructing any passive configuration and computing any μ-recursive function. I have estimated that it will take at least 1.3 million cells, not including any tapes. It is not an attempt to create the smallest universal computer-constructor. A configuration this large would take inordinate amounts of time and space to replicate, not to mention that it has 4 tapes. Here’s how it might replicate: Seek the first tape mark on data tapes 1 and 2, moving the construction arm to the right position. Seek the beginning of data tapes 1 and 2, ignoring all instructions. Seek the end of data tapes 1 and 2, ignoring all instructions, and extending the construction arm by 1 cell every time the tape head moves right by 1 cell. Seek the beginning of data tapes 1 and 2, copying the entirety of data tape 1 using the construction arm. Seek the first tape mark on data tapes 1 and 2, ignoring all instructions. Seek the second tape mark on data tapes 1 and 2, moving the construction arm to the right position. Seek the beginning of data tapes 1 and 2, ignoring all instructions. Seek the end of data tapes 1 and 2, ignoring all instructions, and extending the construction arm by 1 cell every time the tape head moves right by 1 cell. Seek the beginning of data tapes 1 and 2, copying the entirety of data tape 2 using the construction arm. Seek the second tape mark on data tapes 1 and 2, ignoring all instructions. Seek the end of data tapes 1 and 2, passing construction and articulation instructions to the signal discriminator and the construction arm, constructing the daughter automaton, including the program and marker tapes, then initializing and starting the daughter automaton, and finally returning the construction arm to it’s initial state. Seek the beginning of data tapes 1 and 2, ignoring all instructions. Reset the machine, and halt. The tape uses full run-length encoding, *NOT* run-length *limited* encoding. This is mostly to minimize the length of the tape, because an overly long tape can cause slowdown. I might make a smaller one later. 76.232.22.106 (talk) 16:08, 25 August 2018 (UTC) My comparison of implementations Note: May include unreliable information implementation source ruleset rectangular area number of cells length of tape ratio timesteps for replication tape code compression tape code length tape code type replication mechanism replication type growth rate Nobili-Pesavento, 1995 tape.evn Nobili 32-state 97 × 170 6,329 145,315 22.96 6.34 × 1010 none 5 bits binary holistic constructor non-repeatable linear Nobili, 2007 SR_CCN_AP.EVN Nobili 32-state 97 × 100 5,313 56,325 10.60 9.59 × 109 run-length limited encoding 5 bits binary holistic constructor repeatable super-linear Buckley, 2008 codon5.rle Nobili 32-state 112 × 50 3,343 44,155 13.21 5.87 x 109 auto-retraction 5 bits binary holistic constructor repeatable linear Buckley, 2008 replicator.mc von Neumann 29-state 312 × 132 18,589 294,844 15.86 2.61 × 1011 auto-retraction 5 bits binary holistic constructor repeatable linear Buckley, 2008 codon4.rle Nobili 32-state 109 × 59 3,574 37,780 10.57 4.31 x 109 auto-retraction/bit generation 4 bits binary holistic constructor repeatable linear Buckley, 2009 codon3.rle Nobili 32-state 116 × 95 4,855 23,577 4.86 1.63 x 109 auto-retraction/bit generation/code overlay 3 bits binary holistic constructor repeatable super-linear Buckley, 2009 PartialReplicator.mc von Neumann 29-state 2063 × 377 264,321 NA - ~1.12 x 1014 none 4 bits binary partial constructor repeatable linear Goucher & Buckley, 2012 phi9.rle Nobili 32-state 122 × 60 3957 8920 2.25 - auto-retraction/bit generation/code overlay/run length limited 3+ bits ternary holistic constructor repeatable super-linear 76.232.22.106, 2018 Unknown, project not completed von Neumann 29-state ~2,000 × 1,500 ~1,300,000 Unknown Unknown Unknown none(program), auto-retraction/bit generation/run-length encoding(data) 5+ bits (program), 5+ bits (data) binary holistic constructor repeatable linear 76.232.22.106 (talk) 16:43, 25 August 2018 (UTC)

Removed "Constructor theory"

I removed the "Constructor theory" wikilink from the See Also section. There is no published evidence of any connection between the Deutsch/Maletto Constructor Theory and von Neumann's Universal Constructor, or indeed any other concept in the field of cellular automata. If an editor wishes to add it back in, a reliable reference is needed to comply with Wikipedia policies, principally WP:NOR. David Spector (talk) 18:54, 12 September 2022 (UTC) David Spector (talk) 18:54, 12 September 2022 (UTC)