Biological surfaces often exhibit persistent orientation patterns, including whorls, spirals, ridges, and anisotropic fibre arrangements. Such structures are usually interpreted through developmental, genetic, or clinical frameworks. Here we present a qualitative proof-of-concept framework exploring whether a minimal physical description based on active nematic theory can reproduce key structural features of such patterns on curved biological surfaces. We do not model any specific biological system; the aim is to demonstrate minimal sufficiency rather than quantitative biological realism. We model orientation as a nematic order parameter on a curved manifold using a complex order-parameter equation within the complex Ginzburg–Landau universality class. Within this reduced framework, topological constraints, active dynamics, spatial stiffness gradients, and mechanochemical feedback generate spiral defect structures, curvature-dependent defect positioning, and localised scalar accumulation. The simulations suggest that topological defects can act as organising attractors: near-uniform orientation states on closed curved surfaces become dynamically unstable and evolve toward defect-containing configurations, consistent with a dynamical interpretation of the hairy-ball constraint. We further introduce a slow scalar material field representing generic biomaterial accumulation, stiffening, or reduced dynamic accessibility, showing how defect-mediated orientation patterns may become stabilised as material memory or mechanochemical lock-in.
Freddy Brugmans (Tue,) studied this question.