  An explanatory model for the emergence of evolvable units must display
emerging structures that (1) preserve themselves in time (2) self-reproduce and
(3) tolerate a certain amount of variation when reproducing. To tackle this
challenge, here we introduce Combinatory Chemistry, an Algorithmic Artificial
Chemistry based on a minimalistic computational paradigm named Combinatory
Logic. The dynamics of this system comprise very few rules, it is initialised
with an elementary tabula rasa state, and features conservation laws
replicating natural resource constraints. Our experiments show that a single
run of this dynamical system with no external intervention discovers a wide
range of emergent patterns. All these structures rely on acquiring basic
constituents from the environment and decomposing them in a process that is
remarkably similar to biological metabolisms. These patterns include
autopoietic structures that maintain their organisation, recursive ones that
grow in linear chains or binary-branching trees, and most notably, patterns
able to reproduce themselves, duplicating their number at each generation.

Adaptation and Self-Organizing Systems;Neural and Evolutionary Computing;Molecular Networks