Smoothing out contourplot in Gnuplot? - gnuplot

Question

I am trying to plot a simple contour plot (in gnuplot) for the Himmelblau's function using the following code :
f(x,y)=(((x**2)+(y)-11)**2)+(((x)+(y**2)-7)**2)
set xrange [-5:5]
set yrange [-5:5]
set contour base
set cntrparam level discrete 13.59085,25,50,100,150,300,500,1000
set table 'cont.dat'
splot f(x,y)
unset table
reset
set xrange [-5:5]
set yrange [-5:5]
unset key
p './cont.dat' w l lt -1
I get the following plot result:
There are a few problems with the plot which I wish to eliminate:
It shows some horizontal lines in the plot, I don't know why. How can I remove the horizontal lines?
The contour lines are not too smooth. How can I improve there smoothness?
I feel that both the above problems are connected but can't figure out how. Can you please help me understand and hopefully eliminate the problems?
EDIT 1 : I found the answer to question-2, i.e. improving smoothness. I could do it by increasing the isosample. But I still get a lot of horizontal lines as shown in figure below.
But how to remove these horizontal lines? I just want the contour lines for the levels specified.

Answer 1

Here is how you can plot only the contour lines: You must use unset surface, which plots only the contour lines, and view the plot from above with set view map. See also the 2D contour projection plot from the gnuplot demos.
Smoothing can be achieved with set isosamples, but in some way also using e.g. set cntrparam bspline and similar.
So your script becomes:
f(x,y)=(((x**2)+(y)-11)**2)+(((x)+(y**2)-7)**2)
set xrange [-5:5]
set yrange [-5:5]
set contour base
set cntrparam level discrete 13.59085,25,50,100,150,300,500,1000
set isosamples 250
unset surface
set view map
set key out
splot f(x,y)
With the result (using 4.6.3):

Answer 2

I was able to solve both the problems. The solution to Problem-2 I already shared in the edit-1 of question.
For Problem-1, i.e. removing the IsoLines from the contour plot, I should have left the initial blocks of data int he cont.dat files which contain the data for the isolines. Instead, I should have plotted from the Data Block 250 onwards (first 250 blocks of data were from IsoLines because of set isosample 250,250 command).