In contrast to the usual procedure for Tierra-like systems of inoculating the environment with hand-written self-reproducing programs, some models have been modified to look at the spontaneous emergence of self-reproducing individuals (e.g. [Koza 94], [Pargellis 96]). Similar work has also been reported within the framework of a cellular automata model [Chou & Reggia 97]. However, the details of these models are so far removed from anything in the real world that I doubt that they can really tell us anything of scientific value about the origin of life.
Walter Fontana and colleagues have developed a fundamentally more interesting approach with their `artificial chemistry' models (e.g. [Fontana 91], [Fontana et al. 94], [Fontana & Buss 96]). They argue that a formalism is needed in biology (and other areas) for constructive systems (i.e. those where the components are objects whose structure can change as the result of interactions). This should be coupled with classical dynamic systems approaches to form a constructive dynamic systems theory. Such a theory would help us to understand dynamic systems in which new operators can emerge as the system evolves. Some of their latest work in developing such a theory is described in [Fontana & Buss 96]. The relevance of this to the study of open-ended evolution is clear.
Rasmussen and his colleagues have described a similar approach to studying self-organisation ([Rasmussen et al. 90], [Rasmussen et al. 91]), but based upon a formalism similar to the von Neumann machine (as described in Section 3.2.1) rather than the λ-calculus and other formalisms used by Fontana and Buss.3.26 They successfully obtained emergent cooperative structures, but emphasised that the details of such structures depended heavily on the details of the system. However, they do suggest that a number of more general conclusions may be drawn, which may have analogies in prebiotic chemical systems [Rasmussen et al. 91] (pp.245-246). These include: that ``there are certain relations, which need to be fulfilled, between system size, available executions per system update, and initial conditions before the systems are able to support complex cooperative dynamics''; that ``functional stability to perturbations is a product of evolution and not a property of the details of the underlying programmable matter''; that ``cooperation emerges as a natural property of the functional dynamics in systems with constructive dynamics''; that ``simplifying the instruction set below a certain level of complexity inhibits the emergence of higher-order cooperative structures'';3.27 that ``it seems easier to create a reproductive system without genes. The emerging cooperative structures have several properties in common with autocatalytic sets found for catalyzed cleavage-condensation reactions in polymer systems''; and that ``the more low-level the living process is, the more fuzzy the organism-environment distinction appears''.
The approach of Rasmussen et al. can be related to work by Kauffman, Bagley, Farmer and colleagues on artificial chemistries (e.g. [Kauffman 86], [Bagley & Farmer 91]). However, Fontana and Buss claim that their approach (mentioned previously) is more general than these, because it is based upon a theory of object construction (e.g. [Fontana & Buss 96], Section 3). Other recent approaches to building constructive dynamical systems include those suggested by Wolfgang Banzhaf, Peter Dittrich and colleagues (e.g. [Banzhaf 94], [Dittrich & Banzhaf 98]), by Shinichiro Yoshii and colleagues (e.g. [Yoshii et al. 98a], [Yoshii et al. 98b]), and by Yamamoto and Kaneko [Yamamoto & Kaneko 97]. Banzhaf, Dittrich and colleagues, for example, have described experiments with a catalytic self-organising reaction system of binary strings. Their most recent work involves the decoding of these strings as programs which determine how one string reacts with another, which is a similar concept to the idea of emergent operators in Holland's α-Universes.
As a general comment, most of these models do not have any spatial structure (the reactions occur in a well-stirred tank), which might have important consequences for self-organising systems. For example, with no spatial structure there can be no notion of individuality in the organisations which emerge. Also, the models do not necessarily have conservation of matter. However, these are not fundamental limitations, and the models could be modified fairly straightforwardly. Indeed, such modifications have been discussed by some of these authors themselves (e.g. [Fontana & Buss 96], [Dittrich & Banzhaf 97]).
Finally, a handful of computer models of autopoiesis have been described (for example, [Varela et al. 74], [Zeleny 77], [McMullin & Varela 97]), but these have so far met with limited success at achieving sustained autopoietic organisation.