Making bubble graphs with gnuplot

Today, I will try to explain how one can make a bubble graph with gnuplot. This is a low-level hack, and is probably not for the faint-hearted. On another occasion, I will discuss how this can be done in a more convenient way, at the price of producing larger files. (Well, this is true, only if one makes postscript figures, but for raster, like png, it shouldn't matter.)

One of gnuplot's most appealing features (at least, for me) is that the postscript file it produces is actually human-readable, and quite instructive. This makes it possible to easily change the plot even when it is in fact finished in the sense that gnuplot has produced it.
So, if you feel a bit adventurous, you could try to see what can be achieved by manipulating the postscript file. Plot the data points with point type 7 (as a matter of fact, it doesn't really matter which style you use, but in what follows, I will assume that we have point type 7), and redirect the output to a postscript file, i.e., you would have a gnu script as in

reset
unset key
set border back
set terminal postscript eps enhanced
set output 'bubble.eps'
plot 'bubble.dat' u 1:2 w p pt 7 ps 2

Simple enough, isn't it? (Do not forget to reset the terminal, once you are done with the plot. Otherwise, all your consequent graphs will be written to 'bubble.eps'.)

Now, that we have the postscript file, open it in any text editor, and search for the line

/CircleF { stroke [] 0 setdash hpt 0 360 arc }

This should be somewhere around line 161. This is just the definition of point type 7, and this definition is used in the actual plotting of your data, somewhere at the end of the postscript file. We will replace the line above by

/CircleF { stroke [] 0 setdash 0 0 0 arc
<< /ShadingType 3
/ColorSpace /DeviceRGB
/Coords [currentpoint exch hpt 1 mul sub exch hpt 0.2 mul add 0 currentpoint 150]
/Function << /FunctionType 2
/Function { 1 }
/Domain [0 1]
/C1 [ 0.8 0 0 ]
/C0 [ 1 1 1 ]
/N 1>> >> shfill} def

While I am not going to write a tutorial on the postscript language, we could certainly see what this does. What we have to keep in mind is that postscript works on stack variables, i.e., we can access various quantities in a top-to-bottom direction, with the last operand being at the top.

First, we take the current x and y coordinates (this is the first currentpoint instruction), and reverse the order of x and y (exch), subtract the value hpt from x (hpt 1 mul sub), reverse the order again, so we are back to the original x-y order, add 0.2*hpt to y (hpt 0.2 mul add). With this set of operations we defined the centre of the colour of our bubble, which is denoted by the next 0. (So, the centre of colour will be to the left and to the top of the geometric centre. North-west, that is.)

Then we define the origin as currentpoint, and the radius as 150. The next couple of lines define the function type and the domain of this function. /C1 and /C0 determine the colour of the object when the function in question takes on the value of 1 (this will be a bit dark shade of red) and 0 (which will be glowing white). The last line just fills the circle. Now, that we know how this works, we can tweak our figure, if needed. As I said, the size of the bubbles will be determined by the last number on the line beginning with /Coords, and we can move the centre of the colour by changing 0.2 to something else (this would be the y direction), or 1 (x direction). In this way, we can where the light appears to come from. Finally, the colour can be changed by replacing the lines in /C1 and /C0. All in all, we have produced the following figure. While this might appear a bit grainy, this is only an artefact of the postscript viewer. If you print it out, it's going to be all right.

As I promised at the beginning, I will show an easier route to achieving the same result. However, we can already see that since the manipulation of the postscript file doesn't require any prior knowledge about anything, this process can easily be scripted, so that you haven't got to replace the lines by hand every time you want to make bubbles.