Using gnuplot terminal on OSX
Your image looks more like qt than X11, so you could reinstall gnu plot to call the qt graphics library:

brew reinstall gnuplot --with-qt5


That's much simpler than getting XQuartz and X11 running since homebrew installs everything you need.



If you wanted to go X11 for reasons, then here is a nice tutorial and links to the visualization tools that should work on recent OS X versions. 


https://github.com/rdp/ruby_gnuplot


It uses X11 for the visualization and should help you get your graph on.


http://xquartz.macosforge.org/landing/ Install the package that gets downloaded, then
brew rm gnuplot &amp;&amp; brew install gnuplot --with-x11


Then start XQuartz, make a new xterm and run a script like this in the xterm window running gnuplot:

set terminal x11
set title "Some Math Functions"
set xrange [-10:10]
set yrange [-2:2]
set zeroaxis
plot (x/4)**2, sin(x), 1/x


Skip the "set terminal" line if you are using qt as it gets set for you when gnuplot starts. If you need monochrome, you can also set terminal xterm.