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Compute the Flow Starting from a Circle
Visualize the flow starting from a circle using increasing lengths of streamlines.
In[1]:=

Click for copyable input
pts = Table[{0.7 Cos[t] - 0.5, 0.7 Sin[t] - 0.5}, {t, 0, 2 Pi, 

    Pi/15.}];
In[2]:=

Click for copyable input
GraphicsGrid[

 Partition[

  VectorDensityPlot[{Cos[x + y^3], Sin[y + x^3]}, {x, -2, 2}, {y, -2, 

      2}, StreamPoints -> {{pts -> {Thickness[0.012], Black}, 

        Automatic}, Fine, {Backward, Scaled[#]}}, StreamScale -> None,

      Epilog -> Point[pts], Frame -> False, MaxRecursion -> 2, 

     StreamStyle -> None, ColorFunction -> "VisibleSpectrum", 

     ColorFunctionScaling -> {400, 700}, 

     VectorStyle -> {White, "Drop"}, VectorScale -> Small] & /@ {0.05,

     0.15, 0.25, 0.5}, 2], ImageSize -> Large, Spacings -> 0]
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