So in the If[evecs==Re[evecs]
, I want to then change the colour in PlotStyle
of the ParametricPlot3D
s (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!