I just installed gnuplot and I am trying to set the default terminal view. On the wikipedia page for gnuplot, there is an image with a graph:
Which terminal view is shown in the image at the link?
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.
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 && brew install gnuplot --with-x11
Then start XQuartz, make a new xterm and run a script like this in the xterm window running
set terminal x11
set title "Some Math Functions"
set xrange [-10:10]
set yrange [-2:2]
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.