How to change the plot style of several curves, in this manipulate box?

Question

I'm sure this is very easy, but I'm currently unable to make it to work properly. I just need to give different colors and style to the three curves shown in this manipulate box:

fun[gamma_] := Plot[x^2 - gamma x^3,{x, 0, 1},PlotRange -> All]

Manipulate[
    Show[
    {fun[gamma], fun[0],  fun[2]},
    PlotRange -> {{0, 1}, {-1, 1}},
    PlotStyle -> {{Thick, RGBColor[0.40, 0.40, 0.80]}, {Medium, RGBColor[0.40, 0.40, 0.40], Dashed}},
    PlotRangePadding -> None],
    {{gamma, 0.5, "gamma"}, 0, 2, 0.01}
]

Currently, the three curves are having the same color and style. I need the two fixed curves to get a medium thickness, dashed gray color, while the moving curve stays in blue. What's wrong with this simple code? Of course, I could introduce a style parameter into the fun function:

fun[gamma_, style_] := Plot[x^2 - gamma x^3, {x, 0, 1}, PlotRange -> All, PlotStyle -> style]

but is there a simpler way to achieve the same effect?

Answer 1

directives = {Directive[Thick, RGBColor[0.40, 0.40, 0.80]], 
   Directive[Thickness@Medium, Gray, Dashed], 
   Directive[Thickness@Medium, Gray, Dashed]};

If you do not want to make any changes to fun:

1. Epilog + Show

Extract the line primitives from fun[0] and fun[2] and used them Epilog with desired styles:

Manipulate[
 Show[fun[gamma], 
  Epilog -> 
    Thread[{Rest@directives, Cases[#, _Line, All] & /@ {fun[0], fun[2]}}],
  PlotRange -> {{0, 1}, {-1, 1}}, PlotRangePadding -> None],
 {{gamma, 0.5, "gamma"}, 0, 2, 0.01}]

2. Post-processing

ClearAll[replaceStyles]
replaceStyles[dirs_] := Module[{d = dirs}, 
  ReplaceAll[{_Directive, l_Line} :> {Last[d = RotateLeft[d]], l}]]

You can use replaceStyles in two ways:

i. Wrap Show with replaceStyles[directives]:

Manipulate[replaceStyles[directives]@
  Show[{fun[gamma], fun[0], fun[2]}, 
    PlotRange -> {{0, 1}, {-1, 1}}, PlotRangePadding -> None], 
 {{gamma, 0.5, "gamma"}, 0, 2, 0.01}]

ii. Wrap {fun[...],..} in first argument of Show with replaceStyles[directives]:

Manipulate[
  Show[replaceStyles[directives] @ {fun[gamma], fun[0], fun[2]}, 
    PlotRange -> {{0, 1}, {-1, 1}}, PlotRangePadding -> None], 
 {{gamma, 0.5, "gamma"}, 0, 2, 0.01}]

iii. Use it as option setting for DisplayFunction in Show[...]:

Manipulate[Show[{fun[gamma], fun[0], fun[2]}, 
  DisplayFunction -> replaceStyles[directives], 
  PlotRange -> {{0, 1}, {-1, 1}}, PlotRangePadding -> None],
 {{gamma, 0.5, "gamma"}, 0, 2, 0.01}]

3. An alternative post-processing

ClearAll[injectDirectives]
injectDirectives[d_] := MapThread[ReplaceAll[l_Line :> {#, l}]@#2 &]@{d, #} &

Manipulate[Show[
  injectDirectives[directives]@{fun[gamma], fun[0], fun[2]},
  PlotRange -> {{0, 1}, {-1, 1}}, PlotRangePadding -> None],
 {{gamma, 0.5, "gamma"}, 0, 2, 0.01}]

4. A more flexible fun

Alternatively, you can modify fun to take options:

ClearAll[morefun]

morefun[gamma_, o : OptionsPattern[]] := Plot[x^2 - gamma x^3, {x, 0, 1},
 o, PlotStyle -> Directive[Thickness@Medium, Gray, Dashed]]

Manipulate[Show[
  {morefun[gamma, PlotStyle -> Automatic], morefun[0], morefun[2]},
  PlotRange -> {{0, 1}, {-1, 1}},
  PlotRangePadding -> None],
 {{gamma, 0.5, "gamma"}, 0, 2, 0.01}]

If you like you can add additional options:

Manipulate[
 Show[{morefun[gamma, PlotStyle -> Automatic, Mesh -> 5, 
    MeshStyle -> PointSize @ Large], 
   morefun[0], 
   morefun[2, PlotStyle -> {Dashing[Medium], AbsoluteThickness[3]}, 
      ColorFunction -> "Rainbow"]}, 
  PlotRange -> {{0, 1}, {-1, 1}}, 
  PlotRangePadding -> None], 
{{gamma, 0.5, "gamma"}, 0, 2, 0.01}]