# [Gnuplot][1] 4, <s>64</s> <s>62</s> <s>61</s> 60 bytes

    se t pn;se is 80;se xyp 0;sp exp(-(x**2+y**2)/(2*$0**2))w pm

Save the above code into a file named `A.gp` and invoke it with the following: 

`gnuplot -e 'call "A.gp" $1'>GnuPlot3D.png`

where the `$1` is to be replaced with the value of `σ`. This will save a `.png` file named `GnuPlot3D.png` containing the desired output into the current working directory.

Note that this *only* works with distributions of Gnuplot 4 since in Gnuplot 5 the `$n` references to arguments were deprecated and replaced with the unfortunately more verbose `ARGn`.

**Sample output with `σ = 3`:**

[![Sample Output][2]][2]

---

Here is another solution which is much shorter at **47 bytes** than the previous one but not the main answer as I am not sure if it molds to the specifications required. Still, it does the main job of plotting the probability density of the Gaussian distribution in 3 dimensions, so it warrants being out here in my opinion.

    se t pn;se is 80;sp exp(-(x**2+y**2)/(2*$0**2))

This still requires Gnuplot 4 for the same reason as the previous solution.

**Sample output with `σ = 3`:**

[![Sample Output # 2][3]][3]


  [1]: http://gnuplot.sourceforge.net
  [2]: https://i.sstatic.net/nj3HB.png
  [3]: https://i.sstatic.net/SPyvS.png