In this work, we propose FieldVMC: a generalisation of Vascular Morphogenesis Controller (VMC) built on the field-based paradigm of aggregate computing, supporting arbitrary network topologies and dynamics and streamlining principled engineering of self-organising structures. At the core, we redesign the VMC model as a field-based computation, enabling the emergence of organisational hierarchies in a decentralised and asynchronous way. By inheriting key properties of aggregate computing, like scalability, asynchronicity, modularity, and reusability, FieldVMC extends the potential domains of application of the original VMC approach. We show by simulation that FieldVMC enables new novel sorts of phenomena to be captured, studied, and engineered, including: self-construction of tree structures from a single node (germination), self-healing of damaged structures (cutting), self-integration of disjoint structures (grafting), self-segmentation in autonomous sub-structures (budding), and self-optimisation of existing structures (abscission and regrowth).