Chaos, Sdraom & Fmcrals Vol. 5, No. II. pp. 20X9-20513, lYY? Copyright 0 1995 Elsevier Science Lrd Printed in Great Britain All rights rr~rewed OY60-0779/95$Y SO + 000 0960-0779(95)00008-9 Five-fold Quasicrystal-like Germinal Pattern in the Faraday Wave Experiment M. TORRES, G. PASTOR and I. JIMkNEZ Instituto de Electronica de Comunicaciones, Consejo Superior de Investigaciones Cientificas, Serrano 144, 28006 Madrid, Spain F. MONTERO DE ESPINOSA Instituto de Acustica, Consejo Superior de Investigaciones Cientificas, Serrano 144, 28006 Madrid, Spain Abstract -A stable five-fold standing wave pattern exhibiting a germinal quasicrystalline structure has been found for the first time in a symmetry breaking Faraday instability experiment with a low aspect ratio and the liquid depth being less than the surface wavelength. The liquid surface parametric instability when the vessel vibrates vertically is a phenome- non discovered by Faraday which is being revised nowadays in the context of the pattern formation theory [l]. Octagonal [2] and dodecagonal [3] quasicrystalline patterns have been found in the above-mentioned experiment by using inviscid and viscid liquids, respectively, both of them in nonlinear regimes. So far no five-fold quasicrystalline pattern in the Faraday experiment has been found even in an embryonic state. The aim of this paper is to show the existence of these structures in such experiments. In our experiment the vessel is circular and the boundary conditions are free (namely there is a meniscus and there is no frequency selectivity as for the pinned boundary [4]). Thus, the symmetry breaking consists of the infinite symmetry reduction of the synchron- ous circular waves, at the forcing frequency f, and originates in the meniscus with a linear regime to a pattern exhibiting a CsV symmetry and a germinal quasicrystalline topology when the vessel vibration amplitude is greater than the threshold critical value A, in the onset of the instability after the bifurcation. Then, the surface wave frequency reduces to fS = f/2 and th e regime in nonlinear [l]. If we increase the vibration amplitude the pattern remains stable up to a disorder amplitude second threshold Ad. This is the onset of the order-disorder transition [5]. We have used a 10 cm inner diameter Pyrex circular vessel attached to a Brtiel & Kjaer 4291 vibration exciter by means of an aluminium rod screwed to the exciter and glued to the vessel periphery. This simple asymmetric arrangement works well, free of mechanic resonances, due to the low frequency level of our experiment (f in the 30-40 Hz range). The vibrator is excited with a sinusoidal wave generated by a synthesizer. The vibration amplitudes have been interferometrically measured. In our frequency range the measures in three equidistant points of the vessel edge differ less than 3%. The shadowgraphs of the liquid surface are produced by an illumination system located over the vessel and they are projected onto a movable screen below the vessel and videotaped. The liquid used is