How to make sure the graph is “on top” of the old ones?

Question

Manipulate[
    ListPlot[
        {
            Thread[{Range[1, 10, s], Range[1, 10, s]}],
            Range[1, 10, 1]
        },
        Filling -> Axis,
        GridLines -> Automatic,
        GridLinesStyle -> {{Gray, Dotted}, {Gray, Dotted}},
        Frame -> True,
        PlotRange -> {{0.8, 10}, {0, 10}}
    ],
    {s, {1, 0.5, 0.25, 0.125, 0.10}}
]

Default, the s=1 graph is always there (in orange) when clicked on s=0.5, I made it look like the new points in blue are added on.

How could I improve the code, so that when I click on s=0.25, only show the "new points" in a different color? and so on.

For example, when click on s=0.25, the lines from s=1 stay in orange, the lines from s=0.5 stay blue, and the new lines from s=0.25 show in red.

Thanks.

Answer 1

I think this might be what you are looking for:

list = {Thread[{Range[1, 10, 1], Range[1, 10, 1]}]};
snow = 1;
Manipulate[
 If[s != snow, 
  PrependTo[list, Thread[{Range[1, 10, s], Range[1, 10, s]}]]; 
  snow = s];
 ListPlot[list, Filling -> Axis, GridLines -> Automatic, 
  GridLinesStyle -> {{Gray, Dotted}, {Gray, Dotted}}, Frame -> True, 
  PlotRange -> {{0.8, 10}, {0, 10}}], {s, {1, 0.5, 0.25, 0.125, 
   0.10}}]

Essentially, list is now storing the history of what you have plotted before and prepends the new data so it's plotted on top.

You may want to use DeleteDuplicates after the PrependTo command.

Answer 2

Manipulate[pos = Position[slist, s, 1, 1][[1, 1]];
 ListPlot[data[[;; pos]], Filling -> Axis, GridLines -> Automatic, 
  Axes -> False, GridLinesStyle -> {{Gray, Dotted}, {Gray, Dotted}}, Frame -> True, 
  PlotRange -> {{0.8, 10}, {0, 10}}], {{s, First@slist}, slist}, 
 Initialization :> {slist = {1, 0.5, 0.25, 0.125, 0.10}; 
   d1 = Transpose /@ Transpose[{#, #}] &@Range[1, 10, slist]; 
   data = FoldList[Complement[#2, #] &, d1]}]