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I'm trying to plot in the neighborhood of the origin and I can't change the shape and size of the arrows. What I need is to be sure whether or not the solutions are attracted to the line that goes from (0,0,0) to (0,0,1)

VectorPlot3D[{{8 (5 - 6 u)^2 Sqrt[1 - u]
     x (Sqrt[u] x (-1 + z) + Sqrt[1 - u] (-1 + 2 x) z)^2 (-z + 
      x (-1 + 3 z)) (x - z - 2 x z + x^2 (-3 + 9 z)), 
   2 (-5 + 6 u) (1 - z) z (Sqrt[u] x (-1 + z) + 
      Sqrt[1 - u] (-1 + 2 x) z) (-z + 
      x (-1 + 3 z)) (-((-5 + 4 u + 4 Sqrt[-((-1 + u) u)]) (-1 + 
           x) x (-1 + z) z) + 
      8 (-5 + 6 u) x (-1 + 3 z) (z - u z + 
         x (Sqrt[-((-1 + u) u)] - (2 - 2 u + 
               Sqrt[-((-1 + u) u)]) z))), -4 Sqrt[1 - u]
     u (-5 + 6 u) (-5 Sqrt[1 - u] + 4 Sqrt[u] + 4 Sqrt[1 - u] u - 
      4 u^(3/2)) (-1 + x) x (-1 + z) z (Sqrt[u] x (-1 + z) + 
      Sqrt[1 - u] (-1 + 2 x) z) (-z + x (-1 + 3 z))}}, {x, 0, 
  0.01}, {z, 0, 0.01}, {u, 0, 1}, VectorPoints -> 5, 
 VectorScale -> {Automatic, Automatic, Automatic}, 
 AxesLabel -> {x, z, u}].

Thank you in advance for your help

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  • $\begingroup$ Try it with the options ` VectorPoints -> 10, VectorScaling -> Automatic, VectorSizes -> 2, PlotLegends -> Automatic` $\endgroup$
    – eldo
    Commented Oct 5, 2023 at 22:54
  • $\begingroup$ Try VectorMarkers -> "Segment", this will give lines with varying lengths. $\endgroup$
    – Daniel Huber
    Commented Oct 6, 2023 at 9:32

1 Answer 1

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It seems that you want to visualize the vector field in the neighborhood of the origin with specific arrow sizes and shapes. You can achieve this by adjusting the VectorScale and VectorStyle options. Here's how you can modify your VectorPlot3D code to control the arrow sizes and shapes:

VectorPlot3D[{{8 (5 - 6 u)^2 Sqrt[1 - u]
     x (Sqrt[u] x (-1 + z) + Sqrt[1 - u] (-1 + 2 x) z)^2 (-z + 
      x (-1 + 3 z)) (x - z - 2 x z + x^2 (-3 + 9 z)), 
   2 (-5 + 6 u) (1 - z) z (Sqrt[u] x (-1 + z) + 
      Sqrt[1 - u] (-1 + 2 x) z) (-z + 
      x (-1 + 3 z)) (-((-5 + 4 u + 4 Sqrt[-((-1 + u) u)]) (-1 + 
           x) x (-1 + z) z) + 
      8 (-5 + 6 u) x (-1 + 3 z) (z - u z + 
         x (Sqrt[-((-1 + u) u)] - (2 - 2 u + 
               Sqrt[-((-1 + u) u)]) z))), -4 Sqrt[1 - u]
     u (-5 + 6 u) (-5 Sqrt[1 - u] + 4 Sqrt[u] + 4 Sqrt[1 - u] u - 
      4 u^(3/2)) (-1 + x) x (-1 + z) z (Sqrt[u] x (-1 + z) + 
      Sqrt[1 - u] (-1 + 2 x) z) (-z + x (-1 + 3 z))}}, {x, 0, 
  0.01}, {z, 0, 0.01}, {u, 0, 1},
 VectorPoints -> 5, 
 VectorScale -> {0.01, 0.01, 0.01},  (* Adjust arrow size here *)
 VectorStyle -> {{Red, Arrowheads[0.02]}, {Blue, Arrowheads[0.02]}}
 AxesLabel -> {x, z, u}]
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