We argue that attempting to quantify open-endedness misses the point: The nature of open-endedness is such that an open-ended system will eventually move outside its current model of behavior, and hence outside any measure based on that model. This presents a challenge for analyzing Artificial Life systems, leading us to conclude that the focus should be on understanding the mechanisms underlying open-endedness, not simply on attempting to quantify it. To demonstrate this, we apply several measures to eight long experimental runs of the spatial version of the Stringmol automata chemistry. These experiments were originally designed to examine the hypothesis that spatial structure provides a defense against parasites. The runs successfully show this defense, but also show a range of innovative, and possibly open-ended, behaviors involved in countering a parasitic arms race. Commencing with system-generic measures, we develop and use a variety of measures dedicated to analyzing some of these innovations. We argue that a process of analysis, starting with system-generic measures but going on to system-specific measures, will be needed wherever the phenomenon of open-endedness is involved.

We introduce MetaChem, a language for representing and implementing artificial chemistries. We motivate the need for modularization and standardization in representation of artificial chemistries. We describe a mathematical formalism for Static Graph MetaChem, a static-graph-based system. MetaChem supports different levels of description, and has a formal description; we illustrate these using StringCatChem, a toy artificial chemistry. We describe two existing artificial chemistries—Jordan Algebra AChem and Swarm Chemistry—in MetaChem, and demonstrate how they can be combined in several different configurations by using a MetaChem environmental link. MetaChem provides a route to standardization, reuse, and composition of artificial chemistries and their tools.

Automata chemistries are good vehicles for experimentation in open-ended evolution, but they are by necessity complex systems whose low-level properties require careful design. To aid the process of designing automata chemistries, we develop an abstract model that classifies the features of a chemistry from a physical (bottom up) perspective and from a biological (top down) perspective. There are two levels: things that can evolve, and things that cannot. We equate the evolving level with biology and the non-evolving level with physics. We design our initial organisms in the biology, so they can evolve. We design the physics to facilitate evolvable biologies. This architecture leads to a set of design principles that should be observed when creating an instantiation of the architecture. These principles are Everything Evolves, Everything's Soft , and Everything Dies . To evaluate these ideas, we present experiments in the recently developed Stringmol automata chemistry. We examine the properties of Stringmol with respect to the principles, and so demonstrate the usefulness of the principles in designing automata chemistries.