  The evolution of three-dimensional, cellular convective flows in a plane
horizontal layer of a Boussinesq fluid heated from below is well studied. Here
we review results from the investigation of this system as well as a number of
related and novel numerical findings. We present theoretical results for
pattern formation in Rayleigh-B\'enard convection with solving NS equation
under the Boussinesq approximation . System of equations were reduced to
2-dimension form to simplify the analysis.The evolution of the flow agree with
the idea of the flow achieving an optimal form.
