Real Evolution in Arti cial

1 Overview The intention of this contribution is to stimulate discussion concerning the following question: Are artiicial chemistries a useful tool to study pre-biotic or chemical evolution ? Or more general: Are artiicial chemistries a useful tool to study the evolution of organizations ? The latter question implies that the insights gained from the investigation of chemical-like systems can be transfered to other systems which are also forming organizations through local interactions of many components. The rst part gives an introduction to artiicial chemistries. In the second part an example for \real evolution" in an artiicial chemistry is shown. The term \real evolution" refers to the phenomena of self-evolution, where every variation and implicit selection is performed by the individuals (molecules) themselves and not by explicit external selection, mutation or recombination operators. An artiicial chemistry is an artiicial system, which is similar to a chemical system. Usually, an artiicial chemistry consists of: 1. a set of objects S : These objects may be abstract symbols 16], character sequences 1, 12, 14], lambda-expressions 8], binary strings 3, 6, 15], numbers 4], or proofs 10]. 2. a set of rules R, describing the interaction among objects: The rules can be deened explicitly 16, 7] or implicitly by using string matching/string concatenation 2, 13, 14], lambda-calculus 8, 9], Turing machines 15], nite state machines or machine code language 6], proof theory 9], matrix multiplication 3], or simple arithmetic operations 4]. 3. an algorithm A driving the system: The algorithm describes how the rules are applied to a collection of objects (soup/population). The algorithm may simulate a well-stirred reaction vessel with no topology 1, 6, 8], an Euclidean discrete CA-like ((xed) topology 13, 16], a continuous 3-D space 17], or a self-organizing topology 5]. Both, the set of object and the interaction rules, can be deened explicitly or implicitly (e.g. by an algorithm or mathematical expression). An example for an implicit deenition is the number-devision chemistry 4]: In the number-division chemistry the set of objects are natural numbers s S = f2; 3; 4; : : :g. Two objects can interact, if one object can be divided by the other. The result of the interaction is the divisor and the division of the two objects. Thus, R = fs 1 + s 2 =) s 3 js 1 mod s 2 = 0 ^ s 3 = s 1 =s 2 g.