Graphing isosurfaces and field lines

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Graphingisosurfacesandfieldlines.jpg
Graphingisosurfacesandfieldlines.jpg887×797 163 KB

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Great post Chase! Amazing work - I can only imagine where this program can fall in any teaching or visualization setting! wow. It reminds me of Giuseppe’s fluid flow project too…

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Thank you!!

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Thanks so much Theo! It was just a simple demo of how to use the three builtin functions together, StreamPlot3D, ContourPlot3D, and Grad, but I am glad you found it useful. Giuseppe’s fluid flow project was definitely pretty impressive.

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In the Ruliad, @Chase Marangu, Wolfram Ambassador! Force = Gradient Field of Potential Energy.

v[x_, y_, z_] := 
 Sum[1/Sqrt[(x - 10*Cos[i*105])^2 + (y - 10*Cos[i*39])^2 + (z - 
        10*Tan[i*22.1211])^2], {i, 1, 5}]
e[x_, y_, z_] := 
 Evaluate[(-1)*Grad[v[a, b, c], {a, b, c}] /. a -> x /. b -> y /. 
   c -> z]
plotSize = 10;
potentialColorFunction = Function[
   {x, y, z},
   RGBColor[0, 0.5 + 0.5*Sin[v[x, y, z]*30], 1]];
potentialPlot = ContourPlot3D[
   Evaluate[v[x, y, z]],
   {x, -plotSize, plotSize},
   {y, -plotSize, plotSize},
   {z, -plotSize, plotSize},
   Mesh -> None,
   ContourStyle -> Directive[
     RGBColor[0.1, 1, 1],
     Opacity@0.4,
     Specularity[White, 20]
     ],
   Contours -> 10
   ];
fieldPlot = StreamPlot3D[
   Evaluate[e[x, y, z]],
   {x, -plotSize, plotSize},
   {y, -plotSize, plotSize},
   {z, -plotSize, plotSize},
   StreamStyle -> "Line",
   StreamPoints -> Fine,
   StreamScale -> Full,
   PlotRange -> {{-plotSize, plotSize}, {-plotSize, 
      plotSize}, {-plotSize, plotSize}},
   BoxRatios -> {1, 1, 1},
   Boxed -> False,
   Axes -> None,
   Lighting -> "Neutral"
   ];
Show[fieldPlot, potentialPlot, ImageSize -> Large, PlotRange -> All, 
 Boxed -> False]

Oh that’s a nice field this is the best thing that my eyes have ever seen. The demo of how to use the three builtin functions and I do sometimes, I find it useful.

FieldPotential.png
FieldPotential.png1152×1250 403 KB

When you go down to the foundations of things, drill down to the foundation in these scorched sands that’s why it’s so nice to see your post now. Before I get back to my day job you know what you want to do. Thanks for this you have made me feel wonderful.

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I’m so glad to hear you found my post valuable Dean Gladish! Keep experimenting!

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