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In addition to consideration of the general scheme of reproduction, we also have to tackle issues concerning the representation that should be used for the reproducers and for the environment in which they exist. Rasmussen and colleagues have presented a useful survey of different universal formalisms which may be employed, and point out that a spectrum of other formalisms exist in between them [Rasmussen et al. 91].

There is also a choice between procedural and functional representations. Tierra and related systems have used procedural languages with considerable success, although some have argued that functional languages have many desirable properties (see, for example, [Fontana 91]).

Another issue concerns the level at which the model is pitched. Von Neumann argued that a level must be found which is neither too high nor too low:

``If you choose to define as elementary objects things which are analogous to whole living organisms, then you have obviously killed the problem, because you would have to attribute to these parts those functions of the living organism which you would like to describe or to understand ... One also loses the problem by defining the parts too small, for instance, by insisting that nothing larger than a single molecule, single atom, or single elementary particle will rate as a part. In this case one would probably get completely bogged down in questions which, while very important and interesting, are entirely anterior to our problem.'' [von Neumann 49] (p.479).

Similarly, Yaeger points out that the computational power that researchers currently have readily available is not sufficient to enable one to start off at the level of subatomic particles and expect to observe ethological behaviours [Yaeger 94] (p.268). As an example of what is presently achievable, Bernd Mayer and Steen Rasmussen have recently described a system in which emergent third-order structures (micelles) appeared from organised second-order structures (polymers), which in turn appeared from organised first-order structures (monomers)--the monomers being the fundamental level of representation in the simulation [Mayer & Rasmussen 98]. This work (which employed a two-dimensional lattice world of dimensions 100 x 100 units) pushes currently-available computational power to the limit. Finally, Harvey argues that the level of representation should be as low as possible, so as not to introduce the prejudices of the designer or to restrict the evolutionary potential of the system [Harvey 93] (p.48).

The representation of the environment is another issue, and one which has received little attention so far in the artificial life literature. Organisms in Tierra, the α-Universes and many other systems described in this chapter exist in a one-dimensional world; von Neumann's self-reproducing automata, Avida and others are two-dimensional, and several people have tried modelling three dimensions. An important point to note is that there are qualitative differences in the properties of spaces of different dimensionality (e.g. concerning random walks, [Feller 67] pp.359-363). Von Neumann suspected that three dimensions, or a Riemann surface (a multiply-connected plane), might be required for his kinematic model of self-reproduction, although he did not prove it [von Neumann 49] (p.485). Whether or not this is true, though, it is clear that the kinds of phenomena that might evolve in an artificial life model will be constrained by the dimensionality of the model.

More broadly, the basic laws governing components in the system and how they interact, and the spatial structure of the system, will all contribute crucially to how the components evolve. The general idea that more complicated environments lead to more complicated organisms is fairly widely accepted, but we are really only just beginning to investigate the dependencies which exist between these fundamental aspects of an evolving system.

next up previous contents
Next: Design Details of the Up: Methodology and Design Issues Previous: Self-Reproduction
Tim Taylor