At first I thought the Petal Stitch was made up of a Stem Stitch and a Lazy Daisy, then with Deepa's comment I realized the thread goes over the needle which means it is an Outline Stitch. Then I took a closer look and found the stitch line goes from right to left - Stems and Outlines travel in a left to right direction. Have a look at this summery:
I then tried making a line of Outline Stitches with a Lazy Daisy underneath each stitch (as seen in the bottom).
However, I find that the easiest way to stitch IS the traditional way: Stitched from right to left, the thread over the needle and each Lazy Daisy places underneath. So my conclusion is that the linear part of this stitch actually is a BACKWARD OUTLINE STITCH.
Anyway, here is my homework:
Sunday Stitch School Reference Chart
Free stitching on the teal wool tailoring scribble cloth. I liked working in the variegated thread with longer anchoring stitches.
CrazyQstitcher has made great use of the stitch. Go and have a look.