It is safe to deduct that Anima's Symbol that appears in her chamber of Fayth is Darkness. Its in the wall at the opposite side of the room from the door, placed in the center of a circular object with yellow behind it. Above it is the symbol of Yevon, which usually appears on everything that has to do with spira (best example, the floor in the Djose temple).

On Anima's other symbol, the one that glows infront of the door to the chamber of fayth before it shatters, the symbol for darkness also appears. It looks like two eyes crossing eachother, one going vertical and one horzontal. The vertical one is dark, while the horizontal one is light. On the outside of the horizontal one there is the symbol for light, accoding to Water Nymph. I am not sure what the symbol on the outside of the vertical eye is, but i believe it looks similar to fire, which appears in the chamber of fayth at Kilika for Ifrit.

Eyes are used in many cultures as many things. In some, eyes are considered windows into the soul, or even knowledge. Anima's symbol can be taken a number of ways, but Square did it for a particular reason. Anima's attacks are all done through the eye, and when she finishes her attack, it bleeds. Perhaps this is a window into the rage in her soul, and she cries blood because of her pain.

Im not 100% sure this is right, just an opinion on what i know about Anima, different cultures, and the things with the eye. I give credit to Sandy at Water Nymph for her in depth research on the Sanskirt and the writing forms of Spira.