Showing results of the previous value in Manipulate plot

Question

I want to show a multi-variable Manipulate plot with the current and last setting together but not using Bookmarks as I want to show both plots. Is there a way to capture the previous variable values and plot the line for the old values. My attempt does not update the last values.

Manipulate[Plot[{Sin[a x + b], Sin[lasta x + lastb]} , {x, -2 Pi, 2 Pi}, 
    PlotLabel -> Style["ai ="<>ToString[a]<>", bi ="<>ToString[b]<>
    "\n a(i-1) ="<>ToString[lasta]<>", b(i-1) ="<>ToString[lastb], 20]],
    {a, 0, 5} , {b, 0, \[Pi]}, SynchronousUpdating -> False, 
    Initialization :> {lasta = a; lastb = b;}]

This is what I want to achieve ...

Thanks to @belisarius's code here is the persistence view (see code in comments). Could reduce number of lines by using last n added using [[-n;;]] in the plot. Could also add a Reset button see "Reset" Button for Manipulate as Button["Reset", r = {{-5, 0}}]

Answer 1

Manipulate[
 Plot[{Sin[a x + b], Sin[lasta x + lastb]}, {x, -2 Pi, 2 Pi}, 
  PlotLabel -> 
   Style["ai =" <> ToString[a] <> ", bi =" <> ToString[b] <> 
     "\n a(i-1) =" <> ToString[lasta] <> ", b(i-1) =" <> 
     ToString[lastb], 20]],
 {a, 0, 5, TrackingFunction -> {(lasta = a; lastb = b); &, a = #; &, a = #; &}},
 {b, 0, N[Pi], TrackingFunction -> {(lasta = a; lastb = b); &, b = #; &, b = #; &}},
 {{lasta, 0}, None}, {{lastb, 0}, None}]

Answer 2

This can be implemented directly using Dynamics and its second argument. TrackingFunction is new in 10.0, but all what it does is give access to the second argument of dynamics. Since it is not clear if you want the plot to show the last values as the slider is moving, or just when one finished moving the slider, there are two versions. The first one does the same thing as the solution above using tracking function, but using direct dynamics and it updates only at the end of the slider motion. The second one, updates as the slider is moving.

Manipulate[
 Plot[{Sin[a x + b], Sin[lasta x + lastb]}, {x, -2 Pi, 2 Pi}, 
  PlotLabel -> Evaluate@style[a, b, lasta, lastb]],

 Grid[{
   {"a ", Manipulator[
     Dynamic[a, {(lasta = a; a = #) &, (a = #) &, (a = #) &}], {0, 5, .1},
     ImageSize -> Small], Dynamic@a},
   {"b ", Manipulator[
     Dynamic[b, {(lastb = b; b = #) &, (b = #) &, (b = #) &}], {0, Pi, .1}, 
     ImageSize -> Small], Dynamic@b}
   }],
 {{a, 0}, None},
 {{lasta, 0}, None},
 {{b, 0}, None},
 {{lastb, 0}, None},
 TrackedSymbols :> {a, b},
 Initialization :>
  (
   style[a_, b_, lasta_, lastb_] :=
    Style["ai =" <> ToString[a] <> ", bi =" <> ToString[b] <> "\n a(i-1) =" <>
       ToString[lasta] <> ", b(i-1) =" <> ToString[lastb], 20]
   )
 ]

Manipulate[
 Plot[{Sin[a x + b], Sin[lasta x + lastb]}, {x, -2 Pi, 2 Pi}, 
  PlotLabel -> Evaluate@style[a, b, lasta, lastb]],

 Grid[{
   {"a ", Manipulator[
     Dynamic[a, {(lasta = a; a = #) &}], {0, 5, .1}, ImageSize -> Small], 
    Dynamic@a},
   {"b ", Manipulator[Dynamic[b, {(lastb = b; b = #) &}], {0, Pi, .1}, 
     ImageSize -> Small],
    Dynamic@b}
   }],
 {{a, 0}, None},
 {{lasta, 0}, None},
 {{b, 0}, None},
 {{lastb, 0}, None},
 TrackedSymbols :> {a, b},
 Initialization :>
  (
   style[a_, b_, lasta_, lastb_] :=
    Style["ai =" <> ToString[a] <> ", bi =" <> ToString[b] <> "\n a(i-1) =" <>
       ToString[lasta] <> ", b(i-1) =" <> ToString[lastb], 20]
   )
 ]

Answer 3

Manipulate[
 (AppendTo[r, {a, b}];
  Plot[
   {Sin[r[[-1]].{x, 1}],
    Sin[r[[-2]].{x, 1}]},
   {x, -2 Pi, 2 Pi}, PlotLabel -> Length@r]), {a, 0, 5}, {b, 0, π},
 TrackedSymbols :> {a, b}, Initialization :> (r = {a, b};)]