  Collective organisation of patterns into ring-like configurations has been
well-studied when patterns are subject to either weak or semi-strong
interactions. However, little is known numerically or analytically about their
formation when the patterns are strongly interacting. We prove that approximate
strongly interacting patterns can emerge in various ring-like dihedral
configurations, bifurcating from quiescence near a Turing instability in
generic two-component reaction-diffusion systems. The methods used are
constructive and provide accurate initial conditions for numerical continuation
methods to path-follow these ring-like patterns in parameter space. Our
analysis is complemented by numerical investigations that illustrate our
findings.
