The Terrazzo filter won't let you paint in symmetry but will allows you to create kaleidoscope-like designs using a portion of your image. It takes a single tile of your image cropped into shape and repeats, reflects, or flips it a number of times in interlocking symmetrical patterns over the surface of your image. Each Symmetry option gives a different tile shape and tiling pattern. You can then apply it to the image you used to make it or to another image.

Actually i'm using this filter with Corel Photo-Paint (came with it) but there is a plugin for Photoshop.

Terrazzo