We are entering a new era in which software systems are becoming more and more complex and larger. So, the composition of such systems is becoming infeasible by manual means. To address this challenge, self-organising software models represent a promising direction since they allow the (bottom-up) emergence of complex computational structures from simple rules. In this paper, we propose an abstract machine, called the composition machine, which allows the definition and the execution of such models. Unlike typical abstract machines, our proposal does not compute individual programs but enables the emergence of multiple programs at once. We particularly present the machine's semantics and demonstrate its operation with well-known rules from the realm of Boolean logic and elementary cellular automata.