Large chemical reaction networks often exhibit distinctive features that can be interpreted as higher-level structures. Prime examples are metabolic pathways in a biochemical context. We review mathematical approaches that exploit the stoichiometric structure, which can be seen as a particular directed hypergraph, to derive an algebraic picture of chemical organizations. We then give an alternative interpretation in terms of set-valued set functions that encapsulate the production rules of the individual reactions. From the mathematical point of view, these functions define generalized topological spaces on the set of chemical species. We show that organization-theoretic concepts also appear in a natural way in the topological language. This abstract representation in turn suggests the exploration of the chemical meaning of well-established topological concepts. As an example, we consider connectedness in some detail.

This article reviews the growing body of scientific work in artificial chemistry. First, common motivations and fundamental concepts are introduced. Second, current research activities are discussed along three application dimensions: modeling, information processing, and optimization. Finally, common phenomena among the different systems are summarized. It is argued here that artificial chemistries are “the right stuff” for the study of prebiotic and biochemical evolution, and they provide a productive framework for questions regarding the origin and evolution of organizations in general. Furthermore, artificial chemistries have a broad application range of practical problems, as shown in this review.

We examine the qualitative dynamics of a catalytic self-organizing system of binary strings that is inspired by the chemical information processing metaphor. A string is interpreted in two different ways: either (a) as raw data or (b) as a machine that is able to process another string as data in order to produce a third one. This article focuses on the phenomena of evolution whose appearance is notable because no explicit mutation, recombination, or artificial selection operators are introduced. We call the system self-evolving because every variation is performed by the objects themselves in their machine form.