plotting - Set the scale in ColorFunction

The following plot (A)

 ListLinePlot[{0,1,2,3},ColorFunction->"TemperatureMap"]

goes from blue to read.

The following plot (B)

ListLinePlot[{4,5,6,7},ColorFunction->"TemperatureMap"]

goes also from blue to read.

I want the colors to be correlated to the number to be plotted, not the position in the list (as above). Therefore I would like (A) to go from white to yellow (approx.) and (B) from yellow to red (approx.).

How can I make the color to be correlated with the value of the number to be plotted and not the position in the list?

Answer

Your problem is due to the fact, that the default setting is ColorFunctionScaling -> True. You'll have to set ColorFunctionScaling -> False with the downside, that you'll now have to take care of a proper scaling:

ListLinePlot[{0, 1, 2, 3}, ColorFunction -> (ColorData["TemperatureMap", #2/7] &), 
 ColorFunctionScaling -> False]

ListLinePlot[{4, 5, 6, 7}, ColorFunction -> (ColorData["TemperatureMap", #2/7] &), 
 ColorFunctionScaling -> False]

Comments

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functions - Get leading series expansion term?

Given a function f[x] , I would like to have a function leadingSeries that returns just the leading term in the series around x=0 . For example: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x)] x and leadingSeries[(1/x + 2 + (1 - 1/x^3)/4)/(4 + x)] -(1/(16 x^3)) Is there such a function in Mathematica? Or maybe one can implement it efficiently? EDIT I finally went with the following implementation, based on Carl Woll 's answer: lds[ex_,x_]:=( (ex/.x->(x+O[x]^2))/.SeriesData[U_,Z_,L_List,Mi_,Ma_,De_]:>SeriesData[U,Z,{L[[1]]},Mi,Mi+1,De]//Quiet//Normal) The advantage is, that this one also properly works with functions whose leading term is a constant: lds[Exp[x],x] 1 Answer Update 1 Updated to eliminate SeriesData and to not return additional terms Perhaps you could use: leadingSeries[expr_, x_] := Normal[expr /. x->(x+O[x]^2) /. a_List :> Take[a, 1]] Then for your examples: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x), x] leadingSeries[Exp[x], x] leadingSeries[(1/x + 2 + (1 - 1/x...

plotting - Plot 4D data with color as 4th dimension

I have a list of 4D data (x position, y position, amplitude, wavelength). I want to plot x, y, and amplitude on a 3D plot and have the color of the points correspond to the wavelength. I have seen many examples using functions to define color but my wavelength cannot be expressed by an analytic function. Is there a simple way to do this? Answer Here a another possible way to visualize 4D data: data = Flatten[Table[{x, y, x^2 + y^2, Sin[x - y]}, {x, -Pi, Pi,Pi/10}, {y,-Pi,Pi, Pi/10}], 1]; You can use the function Point along with VertexColors . Now the points are places using the first three elements and the color is determined by the fourth. In this case I used Hue, but you can use whatever you prefer. Graphics3D[ Point[data[[All, 1 ;; 3]], VertexColors -> Hue /@ data[[All, 4]]], Axes -> True, BoxRatios -> {1, 1, 1/GoldenRatio}]

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