Investigations of pattern forming mechanisms by Fourier filtering: properties of hexagons and the transition to stripes in an anisotropic system

The properties of patterns in an anisotropic system are studied experimenta lly and numerically in an optical pattern forming system with single-mirror feedback. A controlled anisotropy is introduced by a slit filter in Fourie r space. If the slit width is reduced, a transition between hexagons and st ripes via nonequilateral hexagons and rhomboids is observed. The scenario i s reproduced in numerical simulations. The bifurcation to stripes is found to be supercritical whereas the one to hexagons is subcritical in accordanc e with expectation. The results illustrate the potential of Fourier filteri ng as a tool for investigating mechanisms of pattern formation.