Collective behaviour in nature provides a source of inspiration for engineering artificial systems (e.g. robotics, ecosystems of services), due to their inherent mechanisms favouring adaptation to environmental changes and enabling complex emergent behaviour to arise from a relatively simple behaviour of individual entities. The first-order emergence, also referred to as swarm intelligence, is well studied, while higher order levels of emergent behaviour have not received much attention yet. Second-order emergent behaviour arises from the interactions of individuals, which are themselves the result of first-order emergent behaviour. Dictyostelium discoideum provides a compelling case for studying both first- and second-order emergence. Individual cells move around on their own when there is plenty of food. When food is scarce, cells self-aggregate towards a leading center cell (first-order emergent behaviour) to build a super-organism, similar to a slug. The slug displays properties that none of the cells has on its own (e.g. sensitivity to light and heat). It moves as a whole (second-order emergent behaviour) looking for a suitable place to transform into a fruiting body (also known as sporocarp), where later the cells resume their individual behaviour. This paper focuses specifically on the aggregation and migration phases of Dictyostelium discoideum. We present two agent-based models, implemented in Matlab for first order and Python for second order. They display a series of emergent properties, among others homogeneous aggregation territories size (first order) and merging of slugs or new property as sensitivity to light (second order). Future works involve implementing and experimenting both first- and second-order emergence in swarm robotics, and identification of design patterns for engineering higher order emergent behaviour in artificial systems.