Bénard-Marangoni convection displays a two-dimensional ͑2D͒ hexagonal pattern. A topological analysis of these structures is presented. We describe the elementary topological transformations involved in such patterns ͑neighbor switching process, cell disappearance or creation, and cellular division͒ and the typical defects ͓pentagon-heptagon pair, ''flower'' ͑a cluster of more than three polygons incident on the same vertex͒, etc.͔. Usual topological laws ͑Lewis's, Aboav-Weaire's, Peshkin's, and Lemaître's laws͒ are satisfied. For Von Neumann's law, a modification which takes into account a physical effect specific to the dynamics of Bénard-Marangoni structures ͑selection of average cell size in steady regime͒ has been introduced. We also compare topological correlations in Bénard-Marangoni structures with those derived from biological tissues or simulated structures ͑2D hard disk tessellations, Ising mosaics, distributions of maximum entropy formalism, etc.͒. The agreement is fair for pentagons, hexagons, and heptagons. ͓S1063-651X͑96͒06811-0͔
New experimental results concerning the stability of convective patterns in Bénard–Marangoni convection are presented. The hexagonal pattern usually seems to be the most stable. By means of a new thermal technique a predetermined pattern can be imposed and the evolution of a pattern of rolls thus created is observed. For small depths of the fluid layer, hexagons are very stable but they become less and less so as the depth of the layer increases, whereas the imposed rolls become more and more stable. This is linked to the relative importance of the driving mechanisms—surface tension or buoyancy forces—and may correspond to a change in the order of this nonequilibrium phase transition.
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