Thank you Rohit and Henrik,
Rohit's solution does pretty much what I want. When I use Henrik's solution I get no Frame.
This works:
ListLinePlot[shortCoordinates[[n]], ImageSize -> {128, 128},
Frame -> False, Axes -> False, AspectRatio -> 1,
PlotMarkers -> {{\[FilledCircle], 2}} ] // Framed,
All did was add the // Framed recommended by Rohit and it worked perfectly.
If I use Henrik's suggestion as in:
ListLinePlot[shortCoordinates[[n]], ImageSize -> {128, 128},
FrameTicks -> None, Axes -> False, AspectRatio -> 1,
PlotMarkers -> {{\[FilledCircle], 2}} ] ,
I get my graphs but with no frame.
Finally, if I use Henrik's solution with the addition of // Framed
I get what I want, which is my graphs with a simple black square surrounding them.
Thank you both.
Now, If only I could figure out what most of the graphs use the whole range of [Xmin, Xmax] along the X axis and [Ymin,Ymax} on the Y axis BUT a few graphs (about 4%) use the [Xmin,Xmax] range on the X axis, but only part of the [Ymin,Ymax} on the Y axis
where there is space below Ymin and above Ymax on the Y axis. Any clue?