Place your patchworked square on the corner edge of your chosen base fabric and slice a strip from selvedge to selvedge across the fabric the same width.
Trim any unruly pieces from your square as you go along and save these off-cuts.
Place right-sides together and sew along the short edge adding your square to the end of the strip.
Trim again now and save your off-cut for placing in randomly. If you dont have any off-cuts grab a piece of fabric that you love the look of with your base fabric and cut a sliver (any size wide) of it the same length of the slice you cut into the strip. It could be a fat quarter, a craft print, a piece of silk, a piece of hem you just cut from the summer dress you just shortened or whats left of your sons favourite pyjamas that he has grown out of.
You must love it and it must 'go'.
Skip to step 4 if you dont have any off-cuts. I always have off-cuts though.
Join any off-cuts together if they are wide enough to sew together without being 'eaten' by the machine. Mine are about 2 centimetres wide.
Slice through the base fabric at random or roughly in half like I have. It doesnt matter where at this point.
If you dont want, or like the look of, a thin piece of fabric here you can add a piece of another favourite
fabric to the side of your off-cuts. Some fabrics look nice sliced thinly and others look 'lost'. Stitch it in the centre of the slice.