I love the name of this stitch and fortunately it is also a beautiful stitch so that's good (I would hate if it was an ugly stitch -- that would just be a waste of a good name). Anyhow, Serendipity is a small stitch that fits well into small areas and is relatively simple to compensate. The stitch is especially effective in two different colors and/or types of threads.
The stitch is a two-step process. The first step consists of a series of mosaic stitches but instead of having the Mosaic stitches slant up and to the right these mosaic stitches slant up and to the left. A single canvas thread is skipped in-between these "reverse" mosaic stitches.
Once all of the reverse mosaic stitches have been executed, go back and fill in the spaces in between with a series of three stitches (the first stitch is over two intersections, the second is over one canvas intersection and the third is over two canvas intersections). All these fill-in stitches slant up and to the right. See the diagrams provided here.
The Serendipity stitch -- when done in two different colors -- provides an energetic background but the stitch is also useful for depicting clothing, tile floors/walls, paths and packages.