The current report is explicitly not concerned with the phenomenology which this model chemistry may give rise to. However, in order to put the model properly in context, I will briefly summarise the significant phenomenon which might be anticipated.
First note that the given chemistry might plausibly allow the formation (spontaneously or otherwise) of ``cellular'' structures, consisting of one or more catalyst particles contained within a closed chain of L particles. The boundary or membrane of this structure would be permeable to S; thus, such particles could continue to permeate into the structure. Under the action of the K particles, these would then react to form L particles which would also be trapped within the membrane. Thus, a high concentration of L particles could be built up. On an on-going basis, the membrane will rupture, as constituent L particles disintegrate. However, because of the high concentration of L particles already produced within the membrane, it may be expected that one or more of these will diffuse to the rupture site, and allow a repair (possibly in a different conformation), before the K particle can escape. In this way, such a structure would continuously produce or renew itself, while also discriminating itself from its environment: it would be a (minimal) example of autopoietic organisation.
Incidentally, it is not apparent from this why the composition reaction was specified to require two S particles to generate a single L particle. Granted, if the space is initially filled with S particles plus a small number of K particles, it may be useful to generate some holes as a by product of composition, so as to make motion of particles generally easier; but it would seem equally easy to specify that the initial state of the space already contains a ``reasonable'' concentration of holes, and simplify the composition reaction to generate one L particle from one S particle. It certainly seems to me that there is nothing in the phenomenology outlined above that would rely on this 2:1 ratio in the composition reaction.
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Timestamp: Tue Dec 31 18:43:32 GMT 1996