Self-maintaining membrane
A boundary that repairs itself faster than it diffuses away. The oldest computational model of the thing, read closely, including the rule its own authors left out of the paper.
This card sits in the cellular band because the question at this scale is whether a boundary can hold a distinction against diffusion. The model that answers it is the one Varela, Maturana and Uribe published in 1974, an artificial chemistry of three particle types in which a closed chain forms around a catalyst, decays continuously, and is continuously rebuilt from raw material the chain itself lets through. It is the clearest case on this site of a structure that makes its own boundary out of supply. It is also a cautionary example about what a published demonstration actually establishes, because for over twenty years the published description of the model was not sufficient to rebuild the working model.
On this site a basin is the set of conditions a system comes back from. Push a marble around the inside of a bowl and it rolls back to the bottom; the bowl is its basin, and the rim is its edge, the push beyond which it does not come back. Finding basins, and their edges, is the point of the Laboratory. This membrane has one basin. This is a reading page, so the basin below is the one the published runs report; nothing here was run or measured.
| basin | what it returns to | what pushes it | its edge |
|---|---|---|---|
| 1. The closed membrane | a closed chain of links around the catalyst, same shape | links decaying out of the wall (disintegration probability 0.001 in the reported run) | decay faster than repair |
1. The closed membrane. Links decay wherever they are, so gaps open in the wall all the time. A free link made inside drifts to the gap and bonds into it, and the wall is closed again. In the run McMullin and Varela report, a 12-link membrane in a 15 by 15 space that wraps at its edges, with the disintegration probability at 0.001, the membrane suffered two ruptures between time 0 and time 226 and repaired both with no change of shape ("Why the boundary holds"). The edge: decay faster than repair. No rate for that is known, because the implementation reports give defaults for almost none of their eight probability parameters, so how wide the basin is has not been measured. No crossing on record.
The return needs a rule the 1974 paper left out. A free link may bond only if there is no more than one doubly-bonded link in its immediate neighbourhood ("The rule that was not in the paper"). That lets it close a gap and stops it sticking along an intact stretch of wall. Without the rule, links bond wherever they meet and the interior clogs until there is no room left to make more, which is a second way out of the basin. McMullin recovered the rule in 1997 from the original Fortran. A third way out is removing the catalyst: it is never made inside, so the boundary ends permanently.
Every rule and figure below is quoted from the papers listed at the bottom, with the date read. No simulation on this page and nothing measured here.
What the model is
Substrate (S), catalyst (K) and link (L) on a lattice. McMullin and Varela state the chemistry in three sentences:
- Production. "Two substrate (S) particles may react, in the presence of a catalyst (K) particle to form a link (L) particle."
- Bonding. "L particles may bond to other L particles. Each L particle can form (at most) two bonds, thus allowing the formation of indefinitely long chains, which may close to form membranes. Bonded L particles become immobile."
- Disintegration. "An L particle may spontaneously disintegrate, yielding two S particles. When this occurs any bonds associated with the L particle are destroyed also."
Two further rules do the structural work. Chains are selectively permeable: "Chains of L particles are permeable to S particles but impermeable to K and L particles." And a closed chain "effectively traps" the K or L particles it encloses.
the catalyst makes links from substrate → links bond into a chain → the chain closes → the closed chain holds the catalyst inside → the catalyst makes links from substrate
That loop is the whole object. The boundary is what keeps the catalyst in the place where the boundary gets made, and the substrate it is made from crosses the boundary to reach it.
Why the boundary holds
Nothing about the membrane is static. Links decay wherever they are, so gaps open in the wall as a matter of course: "On an ongoing basis, the membrane will rupture as a result of disintegration of component L particles." What closes a gap is an ordinary free link produced inside, which arrives at the rupture site and bonds into it. The authors put the expectation in exactly those terms, that "there should be a high probability that one of these will drift to the rupture site and effect a repair."
Their run reports it happening. "Between time 0 and time 226 the initial membrane suffers two ruptures which are repaired with no change of membrane morphology." The configuration was a 12-link membrane in a 15 by 15 toroidal space, with the disintegration probability set at 0.001 throughout. Their conclusion is that "this model can exhibit persistent, self repairing, autopoietic reaction networks."
So the tile's phrase is literally the mechanism. Repair outruns decay, or the boundary is gone, and there is no third state in which the wall simply sits there.
The rule that was not in the paper
The 1974 paper presented the model and its figures. When McMullin re-implemented it in the 1990s the thing did not work, and the reason was a rule that had been in the original code and in none of the published accounts of it. His 1997 abstract states it plainly: "an additional interaction (chain-based bond inhibition), not documented in the original description by Varela et al., is critical to the realisation of the autopoietic phenomena." His technical report on the algorithm calls it an important and perhaps crucial interaction, "not included in any previous description of the model", which "has been re-discovered."
Without it, links produced inside bond to each other wherever they happen to meet, and "the interior of the membrane becomes progressively clogged up, until there is no longer space available for further production." The vessel fills with its own boundary material and stops.
The ruleReconstructed by McMullin from the original Fortran, it is a count: "a free L particle can form a bond only if there is no more than one doubly-bonded L particle in its immediate (Moore) neighborhood." A free link sitting in a gap has at most one, because the links on either side of the gap are loose ends and are singly bonded, so it may close the gap. A free link lying alongside an intact stretch of wall has two or more, so it may not stick there. The entire discrimination between repairing the boundary and clogging the interior is carried by that threshold.
And a second oneThe Swarm implementation report adds an inhibition McMullin describes in the same terms, this time keyed to "whether there are any K particles in its (Moore) neighborhood." That is what stops links bonding into a shell around the catalyst and sealing it off from the substrate it needs.
What the omission costs the claim
None of this refutes autopoiesis or the 1974 result. The model ran, the membrane was maintained, and the figures were real. McMullin's own verdict on his correction is that it "does not add to, or modify, the original conceptual foundation of autopoiesis in any significant way."
What it does establish is narrower and worth stating. For more than two decades, the canonical computational demonstration that a boundary can produce and maintain itself was reported in a form from which the boundary could not be produced or maintained. The working object lived in the code. The published object was missing the rule that made it work, on the account of the person who went back to the original source and recovered it.
The lesson generalises past this model. A demonstration of self-maintenance is a claim about a mechanism, and a mechanism is only as checkable as its statement. Where the statement is incomplete, what has been demonstrated is that the authors got it to work, which is a weaker and much less transferable thing than it looks.
SOV Condition 3,
§ 7.2) asks: the links are remade from substrate, inside, by the thing the boundary
encloses. Condition 4 is satisfied and not narrowly, since links decay continuously and every
replacement is paid for in substrate, so there is no regime in which the membrane persists for
free. Condition 2 holds within a tolerance, with ruptures absorbed and morphology preserved
across them. The open question is the catalyst. K is never produced and never
decays. It is exempt from the model's own physics, and asked of K rather than of the links, the
reconstitution question does not close: the vessel cannot make another one, and removing it ends
the boundary permanently. That is Robert Rosen’s question, whether every catalyst a
system depends on is made inside it (Robert Rosen). On the letter of Condition 3 that is not disqualifying, because the
criterion is about identity-bearing boundary constituents and K is not one. It is recorded here as
the place to push, not settled. No sovereignty verdict is claimed on this page.
The part that may generalise
Bond inhibition is not a detail of lattice bookkeeping. It is the rule that decides where a boundary constituent is allowed to become part of the boundary, and it decides it by reading the local state of the boundary that already exists.
That suggests a sharpening worth testing against the rest of the framework. Producing the
constituents may not be the demanding half of a self-produced boundary. Regulating their
incorporation may be. A configuration could hold the full recursion to make its own boundary
material from raw supply and still have no boundary worth the name, because the material assembles
in the wrong places and the vessel fills with it. If that is right, the reconstitution criterion
has a companion condition about placement, and AC₁₁ is already reaching
for it in the phrase "boundary-stabilizing".
Whether that is a real addition or something the existing conditions already contain is not decided here.
What would show this reading wrong
A working implementation of the 1974 model that maintains a membrane with no inhibition rule of any kind would show that the omission was not load-bearing and that the interior clogging McMullin reported was an artefact of his implementation.
A version in which the catalyst is itself produced by the reaction network, from the same raw supply, would close the gap named in the hinge and move the case materially.
A membrane that went on being maintained after the catalyst was removed would break the reading of the circuit given at the top, since it would mean something other than the catalyst was producing links.
Honest limits
This is a reading of published work. Nothing on this page was measured, simulated or replicated here, and this card carries no live panel.
The 1974 paper is cited from its abstract and bibliographic record. The full text was not reachable: the publisher's copy is paywalled and the open mirrors disallow automated retrieval. Everything quoted about the model's rules therefore comes from McMullin's re-implementation and his re-presentation of the algorithm, not from the original.
The implementation reports name eight probability parameters and a per-class mobility factor and give numerical defaults for almost none of them. Any claim about how robustly the membrane is maintained, or how wide the tolerance in Condition 2 actually is, would require the source distribution and a run. Neither is presented here.
Sources
Varela, F. J., Maturana, H. R., & Uribe, R. (1974). Autopoiesis: The organization of living systems, its characterization and a model. BioSystems, 5(4), 187–196. The original model. Cited from its abstract and record; full text not reachable. doi.org/10.1016/0303-2647(74)90031-8
McMullin, B., & Varela, F. J. (1997). Rediscovering computational autopoiesis. Proceedings of the Fourth European Conference on Artificial Life. Source of the three reactions, the permeability rule, the trapping of enclosed particles, the ongoing rupture and repair, the 15 by 15 space, the 12-link membrane, the 0.001 disintegration probability, and the clogging result. eeng.dcu.ie/~alife/bmcm-ecal97
McMullin, B. (1997). Computational Autopoiesis: The Original Algorithm. Santa Fe Institute Working Paper 97-01-001 (Dublin City University Technical Report bmcm9701). Source of the re-discovered interaction and of the bond inhibition rule in its counted form, reconstructed from the original Fortran. santafe.edu working paper 97-01-001
McMullin, B. (1997). SCL: An Artificial Chemistry in Swarm. Santa Fe Institute Working Paper 97-01-002 (Dublin City University Technical Report bmcm9702). Source of the inhibition keyed to neighbouring catalyst particles, the named probability parameters, and the mobility scheme. santafe.edu working paper 97-01-002
McMullin, B. (2004). Thirty Years of Computational Autopoiesis: A Review. Artificial Life, 10(3), 277–295. Consulted for the history of the research programme. doi.org/10.1162/1064546041255548
Related on this site: Living Structures, the column this belongs to; the autocatalytic set, the same question one scale down, where a loop makes more of itself but produces no boundary; and the taxonomy for the axis this card sits on.