  Ad-hoc networks are often deployed in regions with complicated boundaries. We
show that if the boundary is modeled as a fractal, a network requiring line of
sight connections has the counterintuitive property that increasing the number
of nodes decreases the full connection probability. We characterise this decay
as a stretched exponential involving the fractal dimension of the boundary, and
discuss mitigation strategies. Applications of this study include the analysis
and design of sensor networks operating in rugged terrain (e.g. railway
cuttings), mm-wave networks in industrial settings and
vehicle-to-vehicle/vehicle-to-infrastructure networks in urban environments.
