Different colors for Thread in ListPlot

Question

Suppose I have two functions (the actual functions are different than these) defined as

f[i_,k_]:=i^(0.01*k), g[k_]:=2/k

I want to get many Listplots for f vs g. Therefore, I proceed as in the following

plot[j_, k_]:=ListPlot[Thread[{f[j, k], g[k]}], PlotTheme -> "Detailed",FrameLabel -> {"f", "g"}, Joined -> False, FrameTicksStyle -> Directive[Black, 10], PlotMarkers -> "OpenMarkers", Axes -> True, PlotRange -> All, LabelStyle -> Directive[Bold, 10], PlotLegends -> Placed[{k}, {0.15, 0.87}], ImageSize -> Medium]

Now to get a number of Listplots in one frame, I do Show[plot[1,3],plot[1,4],plot[1,5]] etc. The code runs fine, but the issue is with the colors of the plots. I am getting the same color for all plots where one can not distinguish among the correct functions. I tried this option PlotStyle -> {Directive[Green, PointSize[0.1]], Directive[Red, PointSize[0.05]], Directive[Blue, PointSize[0.01]], Directive[Yellow, PointSize[0.07]] too but no success. Is there an easy way so that I get the for each plot a different color while showing them in one frame?

Answer 1

There are multiple ways to archive this but one (using Mathematicas automatic coloring and marker styles) is to use just a single ListPlot command to plot all the points:

plot[jkList_List]:=ListPlot[
   {{f[#[[1]],#[[2]]],g[#[[2]]]}}&/@jkList,
   PlotTheme->"Detailed",
   FrameLabel->"f","g"},
   Joined->False,
   FrameTicksStyle->Directive[Black,10],
   PlotMarkers->"OpenMarkers",
   Axes->True,
   PlotRange->All,
   LabelStyle->Directive[Bold,10],
   PlotLegends->Placed[Row[{#[[1]],",",#[[2]]}]&/@jkList,Right,Top}],
   ImageSize->Medium
]

Which results for plot[{{1, 2}, {1, 3}, {2, 4}, {5, 6}}] in