4D plotting in Gnuplot

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Gnuplot can plot 4D plots i.e. with usual 3D plotting, it can provide independent color axis representing another dimension. For this to work, you have to have data files printed in a special way. Suppose you have 2D grid of coordinates (x1, x2, x3, ...) , (y1, y2, y3, ...), and a z-axis that is a function of x and y. Let us assume that the functional values in those points are (g00,g11,g10, ..), i.e. the data is arranged like

x yz variable
x0 y0 f(x0,y0) g00
x0 y1 f(x0,y1) g01
x0 y2 f(x0,y2) g02
x1 y0 f(x1,y0) g10
x1 y1 f(x1,y1) g11
x1 y2 f(x1,y2) g12
x2 y0 f(x2,y0) g20
x2 y1 f(x2,y1) g21
x2 y2 f(x2,y2) g22


Here, f(x,y) is the z-coordinate. It is better if this coordinate is unique. In case of multiple values of z, the figure becomes too much crowded. The gxy values you can put by hand or generated by a code. (Note that, this single line spacing is very crucial for such plots). Now plot the data file using the command

set pm3d
sp "filename.dat" u 1:2:3:4 w pm3d .


Here is an example of a datafile datafile.tab


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