A search for multiple autocatalytic sets in artificial chemistries based on boolean networks

Populations of strings which interact in ways defined by an artificial chemistry can self-organise spontaneously into an autocatalytic set. This paper considers populations of binary strings with fixed length and a reaction scheme that uses strings as both data (or tape) and machine. Here the machine is a boolean network where some parameters are determined by a string from the population. The input to the machine is given by a second string drawn from the population. In the artificial chemistry based on boolean networks, simulations have revealed a high sensitivity on a probabilistic rate that filters out trivial patterns. By variation of the rate parameter, multiple stable sets have been found. Short string lengths are used here, in order not to rely only on simulations, but also to keep the reaction graph small enough to be able to search for possible autocatalytic sets. A search method has been developed that finds all closed subgraphs of the reaction network, which indicate to a high degree what autocatalytic sets are possible. While simulations most often give only one as a result, the search saves many simulation runs, because it is independent of the initial populations. The resulting number and size of autocatalytic Sets gives information about any freedom of the system to adapt, e.g. when coupling such a system to an environment that can impose constraints. So this description of the behaviour of artificial chemistries appears useful for further artificial studies of molecular evolution and the origin of life