StreamPlot[Evaluate[Grad[Exp[-(u^4+v^4)/4],
{u,v}]],{u,-2,2},{v,-2,2},VectorPoints->Automatic,
VectorColorFunction->(ColorData["DeepSeaColors"][.7(#1^2+#2^2)^.5]&),
ImageSize->500,StreamStyle->Opacity[0.8],
StreamColorFunction->(ColorData["BrightBands"][.7(#1^2+#2^2)^.5]&)]
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