Stencils used to be widely used to decorate walls, textiles and other objects, and the craft is having a resurgence today. They're well-suited to Sims 3 patterns, because they're usually painted with semi-transparent paint in a gradient style, which can be mimicked using semi-transparent channels. In all these patterns, the background color will show through the foreground to some extent.
I offer here two designs, daisies and roses. The daisy pattern is ideal for walls and textiles; the rose design is especially good for wall and floor tiles.
Each design comes in two sizes and "clean" and "dirty" versions. The dirty versions have an adjustable dirt layer. Adjust towards black for heavier dirt, towards white for fading (which is particularly good for these patterns).
In Tile and Mosaic. The dirt layer on the rose design can be adjusted to give a marbled or unevenly glazed look to the tiles. Some floor tile materials in the game will shrink the pattern to the tile, so experiment to get the size you want.
In Paint. The small size works well on clothing; both sizes are good on walls and upholstery.
Delphy and Hysterical Paroxysm for tools and teachings, designs modified from http://free-stencilingpatterns.com/newfreepat.html