I have seen in posts Normalizing histogram bins in Gnuplot that is possible to bin some x samples and plot a histogram, with

binwidth=5
bin(x,width)=width*floor(x/width) + binwidth/2.0
plot 'file.dat' using (bin($1, binwidth)):(1/(binwidth*num_points) smooth freq with boxes

I would like to achieve the same result of that post but with the 2D dataset ((x,y)-points) and plot a type of heat map of that data, for example with heat-map indicating the probability, or intensity (i.e. (number of samples)/(bin area)).

How could I compute the 2d-bin_plot with Gnuplot?

Thank you very much for your help