Export["levelsets.gif",
 Table[Plot3D[x^3 + y^3 + x y, {x, -1, 1}, {y, -1, 1}, MeshFunctions -> (#3 &),
   Mesh -> {{c}}, MeshStyle -> {Thick, Black}, PlotPoints -> 50,
   Lighting -> "Neutral",
   ColorFunction -> (ColorData["Rainbow"][#3] &)], {c, -(1/4), 1/20, 1/80}]]