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So in the If[evecs==Re[evecs], I want to then change the colour in PlotStyle of the ParametricPlot3Ds (say, green if eval<0, orange if eval==0 and red if eval>0). As you can see, I've already tried to add another If statement but it doesn't quite appear to be doing exactly what I want. 

Manipulate[{evals, evecs} = 
Eigensystem[({{-\[Sigma], \[Sigma], 
  0}, {r - X[[3]], -1, -X[[1]]}, {X[[2]], X[[1]], -\[Beta]}})];
GraphicsColumn[{Show[
If[evecs == Re[evecs], 
 ParametricPlot3D[
  Evaluate[ConstantArray[X, 3] + t*evecs], {t, -2, 2}, 
  PlotStyle -> {{If[evals < 0, Green, Red]}}], {}], 
Graphics3D[{PointSize[0.025], Red, Point[X]}], 
ImageSize -> {275, 275}]}], 
Row[{Spacer[60], 
Dynamic[Style[
 Text@TraditionalForm[
   HoldForm[({{x}, {y}, {z}})' == 
     Dynamic[Round[({{-\[Sigma], \[Sigma], 
           0}, {r - X[[3]], -1, -X[[1]]}, {X[[2]], 
           X[[1]], -\[Beta]}}), 0.01]] ({{x}, {y}, {z}})]], 
Medium]]}], Delimiter, {{r, 1, Style["r", Medium]}, 0, 40, .1, 
Appearance -> "Labeled", 
TrackingFunction -> ((r = #; updateFN[]) &)}, {{\[Beta], 8/3, 
Style["\[Beta]", Medium]}, 0, 20, .01, Appearance -> "Labeled", 
TrackingFunction -> ((\[Beta] = #; updateFN[]) &)}, {{\[Sigma], 10, 
Style["\[Sigma]", Medium]}, 0, 50, 5, Appearance -> "Labeled", 
TrackingFunction -> ((\[Sigma] = #; 
  updateFN[]) &)}, Delimiter, {{X, {0, 0, 0}}, 0, 1, 
ControlType -> None}, {{X0, 1, 
"Fixed Point:"}, {1 -> "\!\(\*SubscriptBox[\(C\), \(0\)]\)", 
2 -> "\!\(\*SubscriptBox[\(C\), \(+\)]\)", 
3 -> "\!\(\*SubscriptBox[\(C\), \(-\)]\)"}, RadioButtonBar, 
TrackingFunction -> ((X0 = #; updateFN[]) &)}, Delimiter, {evecs, 
ControlType -> None}, {evals, 
ControlType -> None}, {{updateFN, updateFN}, 
ControlType -> None}, Delimiter, ControlPlacement -> Left, 
AutorunSequencing -> {1, 2, 3, 5}, 
Initialization :> (updateFN[] := (X = {{0, 0, 
     0}, {Sqrt[\[Beta]*(r - 1)], Sqrt[\[Beta]*(r - 1)], 
     r - 1}, {-Sqrt[\[Beta]*(r - 1)], -Sqrt[\[Beta]*(r - 1)], 
     r - 1}}~Part~X0; {evals, evecs} = 
  Eigensystem[({{-\[Sigma], \[Sigma], 
      0}, {r - X[[3]], -1, -X[[1]]}, {X[[2]], 
      X[[1]], -\[Beta]}})];);
updateFN[])]

Thank you in advance for your help!

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3
  • $\begingroup$ Isn't evals a list of numbers? If so, evals < 0 won't work. $\endgroup$
    – Michael E2
    Commented Jan 9, 2018 at 20:44
  • $\begingroup$ @MichaelE2 but it will plot 3 different lines. I want the corresponding eigenvalues (so the eigenvalues with the same index) to control the colour of the PlotStyle. I do recognise that what I've done is incorrect. I'm interested in how it should be instead. $\endgroup$
    – Jelmes
    Commented Jan 9, 2018 at 20:47
  • $\begingroup$ I see. I misunderstood what you were after. Something like Sign[evals] /. {-1 -> Green, 0 -> Orange, 1 -> Red}, maybe? $\endgroup$
    – Michael E2
    Commented Jan 9, 2018 at 21:04

1 Answer 1

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3
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So, the answer is

PlotStyle -> Table[Which[evals[[i]] < 0, Green, evals[[i]] == 0, Orange, 
 evals[[i]] > 0, Red], {i, 3}]]
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