Architectural self-organisation, in which different configurations of software modules are dynamically assembled based on the current context, has been shown to be an effective way for software to self-optimise over time. Current approaches to this rely heavily on human-led definitions: models, policies and processes to control how self-organisation works. We present the case for a paradigm shift to fully emergent computer software which places the burden of understanding entirely into the hands of software itself. These systems are autonomously assembled at runtime from discovered constituent parts and their internal health and external deployment environment continually monitored. An online, unsupervised learning system then uses runtime adaptation to explore alternative system assemblies and locate optimal solutions. Based on our experience to date, we define the problem space of emergent software, and we present a working case study of an emergent web server. Our results demonstrate two aspects of the problem
space for this case study: that different assemblies of behaviour are optimal in different deployment environment conditions; and that these assemblies can be autonomously learned from generalised perception data while the system is online.