Document: Computational Autopoiesis: The Original Algorithm

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2 Overview of the Model

The model consists of a two dimensional space, with a discrete square lattice; each lattice position is either empty (referred to as a ``hole'') or contains one ``particle''[2] of one of the defined chemical species or ``elements''.[3] The size of the space is not explicitly restricted or stipulated, but the illustrated example implementation in (Varela et al. 1974) is sized at tex2html_wrap_inline1441 . On the other hand, EXP29.FOR implemented a tex2html_wrap_inline1443 space (albeit, this is largely parameterised, and would not be too difficult to change). Thus, it may be that the diagrams of (Varela et al. 1974) show only a part of a larger, simulated, space.

Behaviours at the edges of the space are not specified in detail, but it seems that the edges are to be regarded as hard limits or boundaries to the space--in the sense that particles cannot move through or across the edges. This would be consistent with the behaviour implemented in EXP29.FOR.

The particles engage in dynamic interactions based (roughly) on discrete timesteps. On each timestep, particles may move and/or engage in a reaction.[4]

There are three distinct chemical species:

Substrate: S
Catalyst: K
Link: L

These participate in three distinct reactions:

  1. Composition:


    In essence, this is a reaction in which two particles of S combine to produce one particle of L. However, the reaction is specified to occur only with the mediation of catalyst, K. The reaction will only occur when two particles of substrate are directly adjacent both to each other and a particle of catalyst. The catalyst particle is unaffected by the reaction (hence its name).

  2. Disintegration:


    This is a reverse reaction to composition. It occurs spontaneously, with a fixed probability per link, per timestep. It is independent of whether the link is bonded or not (see reaction 3).

  3. Concatenation (Bonding): L particles can bond or polymerise into indefinitely long chains.[5] Each L can form at most two bonds. This is a spontaneous reaction, relying only on physical adjacency of two links each of which has either zero or one bond already. There is no reverse, ``unbonding'', reaction per se. Such chains will be broken down again only if or when constituent links spontaneously disintegrate back to substrate (when any associated bonds will also decay).

S, K and free (unbonded) L particles move essentially in random two-dimensional walks--except to the extent that other particles get in the way. This yields something approximating a well-stirred mixture. However, L particles which are bonded (whether single or doubly) do not move at all.[6] It is specified that S particles can permeate through chains of bonded L particles; but L and K particles cannot.

This model ``chemistry'' is, of course, highly abstract and schematised. Specifically, space and time are both discrete; motion is limited to random walks; there are no substantive analogs of newtonian mechanics, such as mass, force, energy etc.

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Document: Computational Autopoiesis: The Original Algorithm

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Timestamp: Tue Dec 31 18:43:32 GMT 1996