There seems to be something in these depressions that is not conducive to the growth of these branches, perhaps more frost (I prefer the word branches as all it implies is that something is splitting from one part into two or more while spider legs don't split into others). I note the branches on the two sides are somewhat different. The branches usually grow out of clumps which are either along the rim or the rim itself has broken into clumps.
Now for a way out idea. As I mentioned before there are many eroded structures even around the equator that resemble these branches, possibly implying an "ice age" there. Perhaps some of the terraces seen are not sedimentary or formed by moving glaciers, but that these branches somehow also form these terraces and did so in this same "ice age".
For example:

http://barsoom.msss.com/moc_gallery/m13_m18/images/M14/M1401848.html

This one shows branches associated with all the various tyes of polar landforms.

http://barsoom.msss.com/moc_gallery/m07_m12/images/M10/M1003277.html