Gnuplot: Scatter plot and density

I have x- and y-data points representing a star cluster. I want to visualize the density using Gnuplot and its scatter function with overlapping points.

I used the following commands:

 set style fill transparent solid 0.04 noborder
 set style circle radius 0.01
 plot "data.dat" u 1:2 with circles lc rgb "red"

The result:

However I want something like that

Is that possible in Gnuplot? Any ideas?

(edit: revised and simplified)

Probably a much better way than my previous answer is the following: For each data point check how many other data points are within a radius of R. You need to play with the value or R to get some reasonable graph.

Indexing the datalines requires gnuplot>=5.2.0 and the data in a datablock (without empty lines). You can either first plot your file into a datablock (check help table) or see here: gnuplot: load datafile 1:1 into datablock

The time for creating this graph will increase with number of points O(N^2) because you have to check each point against all others. I'm not sure if there is a smarter and faster method. The example below with 1200 datapoints will take about 4 seconds on my laptop. You basically can apply the same principle for 3D.

Addition: (contour plot)

• once you have the density data (x:y:density), you can either create a "3D"-splot or a 2D-contour plot
• gnuplot has the feature dgrid3d for this and you need to play with the dgrid3d options (check help dgrid3d), e.g. gauss <number>
• a disadvantage of using splot and set view map is the arrangement/alignment of the margins. Better would be plot, but then you have to plot your generated contours first into another datablock.

Script: requires gnuplot>=5.2.5, Oct. 2018 (because of splot ... nosurface)

### 2D density color and contour plot
reset session

# create some random test data
t0 = time(0.0)
set table $Data
    set samples 700
    plot '+' u (invnorm(rand(0))):(invnorm(rand(0))) w table
    set samples 500
    plot '+' u (invnorm(rand(0))+2):(invnorm(rand(0))+2) w table
unset table
print sprintf("Data creation: %.3f sec",(t1=time(0.0))-t0,t0=t1)

stats $Data u 0 nooutput   # get number of datalines
Rows = STATS_records
R    = 0.7                 # Radius to check

# for each datapoint: how many other datapoints are within radius R
distance(x0,y0,x1,y1) = sqrt((x1-x0)**2 + (y1-y0)**2)
set print $Density
    do for [i=1:Rows] {
        x0 = real(word($Data[i],1))
        y0 = real(word($Data[i],2))
        c  = 0
        stats $Data u (distance(x0,y0,$1,$2)<=R ? c=c+1 : 0) nooutput
        d = c / (pi * R**2)
        print sprintf("%g %g %d", x0, y0, d)
    }
set print
print sprintf("Density check: %.3f sec",(t1=time(0.0))-t0,t0=t1)

set size ratio -1
set palette rgb 33,13,10
set cblabel "points per unit area"

set multiplot layout 1,2
    plot $Density u 1:2:3 w p pt 7 lc palette z notitle

    set dgrid3d 100,100 gauss 0.2
    set contour
    set cntrparam levels 10
    set view map
    set size ratio -1
    set grid x,y
    set key noautotitle out samplen 1
    unset colorbox
    set margins 0,0,0,0
    splot $Density u 1:2:3 w l palette z nosurface
    print sprintf("Contour plot:  %.3f sec",(t1=time(0.0))-t0,t0=t1)
unset multiplot
### end of script

Result:

Data creation: 0.079 sec
Density check: 4.620 sec
Contour plot:  0.889 sec