They are a work of art called "moments" by Carl Trominski. Here is some info about it:
City of Austin.
also
Blue Panels on Lamar Underpass | Austin Metblogs. The concept for the art sounds much more exciting than the actual result.
There is also a mural painted in the center support of that bridge. It is a memorial by a mother to her son --
mary boyd
It was accidentally painted over by city workers (it had achieved "do not touch" status) in 2001, but she came back and painted it again. I think it is now an "art in public places" protected piece now, but I can't find it on the city AIPP list.