  We show that, in round spheres of dimension $n\geq3$, for any given
collection of codimension 2 smooth submanifolds
$\mathfrak{S}:=\{\Sigma_1,...,\Sigma_N\}$ of arbitrarily complicated topology
($N$ being the complex dimension of the spinor bundle), there is always an
eigenfunction $\psi=(\psi_1,...,\psi_N)$ of the Dirac operator such that each
submanifold $\Sigma_a$, modulo ambient diffeomorphism, is a structurally stable
nodal set of the spinor component $\psi_a$. The result holds for any choice of
trivialization of the spinor bundle. The emergence of these structures takes
place at small scales and sufficiently high energies.
