The 3rd element of a tick specification is the pair {plen, mlen}, where plen is the length in the positive direction (i.e., inside for frame ticks), and mlen is the length in the negative direction (i.e., outside for frame ticks). So, create one’s own ticks and use FrameTicks:




Lengths of major and minor ticks can be set this way also.

Better tick support is needed so that licks on different scales (e.g., log, inverse, etc.) can be easily created by the user. An option to a function that creates the ticks could easily specify whether they were in the inside or outside of the frame.
Bob

For controlling ticks on a frame you should not use the option Ticks but FrameTicks, in your case:

FrameTicks -> None

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?