How to do ListDensityPlot using this kind of colorfunction?

Question

I would like to plot a figure using this kind of colorfunction in Mathematica. I opened the "Color Schemes" from the Palettes menu, but did not find a proper colorfunction.

Answer 1

Here I've extracted a long thin part of your image to get the colours. Then I use the value provided by default ColorFunctionScaling from 0 (blue) to 1 (red), to extract the nearest colour or clip to the colours at the endpoints:

(* get the image and smooth it out to reduce the banding effects *)
img = GaussianFilter[Import["https://i.sstatic.net/fJlC6.png"],11];

(* Take a slice of the image from top to bottom, ignoring black and white parts, then reverse *)
colours = Reverse[ImageData[ImageTake[img, {105, -185}, {100, 120}]][[All, 1]]];

(* scaled from 0 (-50) to 1 (0) *)
scale = Length[colours];
(* select the part of the list near scaled up 'v' and clip to ends if necessary *)
mycf[v_] := RGBColor@colours[[Round[Clip[v*scale, {1, Length[colours]}]]]]

DensityPlot[-x y, {x, 0, 7}, {y, 0, 7}, ColorFunction -> mycf, PlotPoints -> 40]