I once heard that symmetry enhances beauty. In abstract digital art I sometimes prefer to mirror each side our 4 quarters of the image. Once an abstract texture with expressive colors reaches a level of intensity I try mirroring that image in different ways. Sometimes I decide to keep the symmetry and other times I opt out on mirroring the image. I listen to my emotional reaction to the piece I am making. My emotions become a rudder to steer the creative direction of the art. View my gallery focusing on symmetry in digital art below.
In GIMP (GNU Image Manipulation Program) I found it very easy to create symmetry. Simply increase the size of the canvas by 200% and then match the layer size to the size of the canvas (there is a menu item just for that) Ensure empty image area remains transparent. Then horizontally or vertically flip the layer. After that merge the visible layers (just the two your working with here). Now you have horizontal or vertical symmetry in GIMP! I do the same process for Photoshop except I just use the guide lines instead of matching the layer to the size of the canvas.