Saturday, 9 May 2009

Multiple layers on the same plot

This time, we will look at how to plot in three dimensions in an appealing way. For the sake of example, I will take the time evolution of the amplitude of water ripples after a point-like disturbance upsets the surface. Without going into details, I simply assume that the surface can be described by the zeroth Bessel function.

As a couple of times before, we will use multiplot to align the various figures. Here is the code

reset
set palette rgbformulae 33, 13, 10
set cbrange [-0.3:1]
a=-0.1
b=0.13
set multiplot
unset ztics
unset xtics
unset ytics
set size 1.1, 0.5
set samples 100,100
set isosamples 100, 100
set origin 0,a
set border 0
unset colorbox
unset key
set view 55,30
set xlabel 'x'
set ylabel 'y'
sp besj0(x*x+y*y) w pm3d at b
unset xlabel
unset ylabel
set origin 0,a+b
sp besj0(x*x/1.2+y*y/1.2)/1.2 w pm3d at b
set origin 0,a+2*b
sp besj0(x*x/1.4+y*y/1.4)/1.4 w pm3d at b
set origin 0,a+3*b
sp besj0(x*x/1.65+y*y/1.65)/1.65 w pm3d at b
set origin 0,a+4*b
sp besj0(x*x/1.95+y*y/1.95)/1.95 w pm3d at b
set origin 0,a+5*b
set arrow 1 from screen 0.1, 0.1 to screen 0.1, 0.8
set label 1 "time" at screen 0.08, 0.45 centre rotate by 90
sp besj0(x*x/2.2+y*y/2.2)/2.2 w pm3d at b
unset multiplot

And here is the figure that it produces


As you can see, as time goes on, the waves move radially outwards. (You shouldn't be carried away by the exact time evolution. This is only a demonstration:) Basically, we plot the functions on maps, and each time we translate the position of the new plot.

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