Patches are not always used to recognize one's own or someone else's, but also just for beauty, such patches are called "Moral".   

To boost morale, military personnel and airsoft players sometimes use Moral Patches like this. This patch is fixed with Velcro on your equipment.   

These patches do not crumple, fade or tear due to the fact that they are made of polymer materials. Fabric is used in a variety of colors.