In[12]:=
f[x_, y_] := x - y^2 Cos[y] contourData = Map[First, Cases[Graphics[ ContourPlot[f[x, y], {x, -10, 10}, {y, -10, 10}, Contours -> {0}, PlotPoints -> 50]], _Line, Infinity]]; Show[Graphics[Map[Line, contourData]]];
If your output will be a sequence of graphs, select a display option.
Display as:
individual images
a movie
both of the above
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1. Harvesting the Seeds