Probably most chess players will have the intuitive notion of what kind of positions are not "tension-filled" and what kind of positions are. Usually these are middlegame positions.
Here's an idea of what kind of positions are "tension-filled": In the position there are many pieces that are either hanging or, many times, a piece of lower material value attacks a piece of higher material value (which may or not be defended). Perhaps it could be defined in such a way as "the total value of hanging pieces plus the total value of defended pieces which are attacked by pieces of inferior material value minus the material value of the pieces of inferior material value attacking the defended pieces", or something like this. This is just a "materialistic" attempt to define the concept, since it doesn't incorporate advantages or disadvantages due to positional factors. Perhaps one could consider Tal vs Hecht, 1962 Varna Olympiad at move 21 as an example of a complicated position.
Nonetheless, is there actually an "objective" or "mathematical" way to quantify this idea which can distinguish a position which is not so complicated from one which most chess players would intuitively agree is "complicated"? Has this been done before?