Online at stacks.iop.org/Non/16

We study steady-state pattern-forming instabilities on R2. A uniform initial state that is invariant under the Euclidean group E(2) of translations, rotations and reflections of the plane loses linear stability to perturbationswith a non-zero wavenumber kc. We identify branches of solutions that are periodic on a square lattice that inherits a reducible action of the symmetry groupD4T 2. Reducible group actions occur naturally when we consider solutions that are periodic on real-space lattices that are much more widely spaced than the wavelength of the pattern-forming instability. They thus apply directly to computations in large domains where periodic boundary conditions are applied. The normal form for the bifurcation is calculated, taking the presence of various ‘hidden ’ symmetries into account and making use of previous work by Crawford [8]. We compute the stability (relative to other branches of solutions that exist on this lattice) of the solution branches that we can guarantee by applying the equivariant branching lemma. These computations involve term