The one on the left _is_ symmetrical. The one on the right may be symmetrical - I can't see enough of it to tell. Remember that "symmetrical"simply means that there are pivots in the tartan across which the tartan repeats in mirror image. A fabric with warp and weft which are not identical, such as the fabric on the right, can still be symmetrical, but it isn't tartan (although some of the Welsh tartans don't have identical warp and weft and we still call them tartan, but virtually all tartans have identical warp and weft).