Individual point coloring in ListPlot, ErrorListPlot in Mathematica

Question

I can get a colored ListLinePlot by doing something like

ListLinePlot[Range[420, 680, 20], ColorFunction -> "VisibleSpectrum", ColorFunctionScaling -> False]

However, as indicated by the help file ("ColorFunction requires at least one dataset to be Joined"), if I do the equivalent

ListPlot[Range[420, 680, 20], ColorFunction -> "VisibleSpectrum", ColorFunctionScaling -> False]

all my points are blue. Is there a nice way to get ColorFunction to work for ListPlot with Joined -> False?

That is, is there a nicer way to get something like

ListPlot[
 List /@ Transpose[{Range[(680 - 420)/20 + 1], Range[420, 680, 20]}], 
 PlotMarkers -> ({Graphics[{#, Disk[]}], 0.05} & /@ ColorData["VisibleSpectrum"] /@ Range[420, 680, 20])
]

?

(Also, does anyone have an explanation of why Mathematica requires Joined -> True in order to make use of ColorFunction?)

Edit: I'm also looking for a way to do a similar coloring with ErrorListPlot in the ErrorBarPlots package.

Answer 1

The problem is, that Joined->True draws a Line[] which can be given VertexColors for each containing point. I assume doing the same for the points when setting Joined->False leads to situations where it does not work. Nevertheless, Line[] and Point[] work pretty much the same in your case. So what is about

ListLinePlot[Range[420, 680, 20], ColorFunction -> "VisibleSpectrum", 
  ColorFunctionScaling -> False] /. Line[arg___] :> Point[arg]

And, by the way, if your using a ListLinePlot only, where the only Line[] directives arising are the one from your data, this should work even if you have more datasets and {x,y} coordinates

data = Transpose[Table[{{x, Sin[x]}, {x, Cos[x]}}, {x, 0, 2 Pi, 0.2}]];
ListLinePlot[data, ColorFunction -> Hue] /. Line[arg___] :> Point[arg]

Answer 2

You can use DiscretePlot:

data = Range[420, 680, 20];
DiscretePlot[data[[i]], {i, Length[data]},
   ColorFunction -> "VisibleSpectrum", ColorFunctionScaling -> False,
   Filling -> None]

If you're plotting a list of x,y points, it gets a little trickier:

data = Transpose[{Range[420, 680, 20], Range[400, 530, 10]}];
mapping = Apply[Rule, data, 2];
DiscretePlot[i/.mapping, {i, data[[;;,1]]},
   ColorFunction -> "VisibleSpectrum", ColorFunctionScaling -> False,
   Filling -> None]

It does seem rather odd that DiscretePlot will let you color the points differently whereas ListPlot won't. I'm sure it must have something to do with the implementation details, but I can't think of a reason why that would be the case.