Though there are many crochet stitch patterns, and they can be known by many names and variations, the Picot Fans stitch pattern is not one of them. It is remarkably standardized by name (in the stitch dictionaries that use names) and I have found only two minor variations in any dictionaries so far. (See comparison of dictionaries at end of this entry.)
It forms a wide decorative band on the hem and sleeves of the new "Helon Dress"; pattern is available in Rowan Yarn's new summer 2008 pattern book. You can also see a full-size pic of it on the first page of the Spr-Sum'08 issue of Vogue Knitting.
For the sleeves of the Baroque Tabard I wanted a richer, more dramatic, more baroque version of Picot Fans, so instead of a (ch 3, sl st in 3rd ch from hook) type of picot, I used a (ch 4, sc in base dc) picot; I like to work the sc into one front loop and one side loop of the base stitch to add a subtle defined ridge to the fan. I also developed a way to work it in the round with turning after only some rounds for design reasons: I wanted all picot and dc rows to be facing the right side of the garment. (I also added an 8th picot to each fan in case it wasn't 'baroque' enough already.)
Jane Rimmer, CGOA member extraordinaire, wrote a wonderful post for Crochetpartners members in which she compared the many ways to make picots.
Dictionaries in which "Picot Fans" appears:
Donna Kooler's Encyclopedia of Crochet, p. 147
Harmony Guides v.6 (1998), p.65
A Japanese dictionary with "Crochet 262 Patterns" on the cover, p. 82
280 Crochet Shell Patterns by Darla Sims (2006), p.42 (Row 3 varies slightly)
The Complete Book of Crochet Stitch Designs by Linda P. Schapper (reissued 2007), p.166 (picot varies slightly)
Some stitch pattern collections in which "Picot Fans" does not appear:
The Complete Encyclopedia of Needlework by Therese de Dillmont (1886; 1978 reprint)
A Treasury of Crochet Patterns by Liz Blackwell (1971)
A Complete Guide to Crochet Stitches by Mary Dawson (1972)
Crochet and Creative Design by Annette Feldman (1973)
Handmade Lace and Patterns by Annette Feldman (1975)
Stitches, Patterns and Projects for Crocheting by Wanda Bonando (1978)
New Directions in Crochet by Anne Rabun Ough (1981)
Vogue Dictionary of Crochet Stitches by Anne Matthews (1992 reprint)
Crochet Stitch Bible (German ed.: Die Hakel-Enzyklopadie) by Betty Barnden (2004)
The Complete Book of Crochet by Pam Dawson (1985) has something called "Shell Arch Pattern" (p.156) which is like Picot Fans minus the picots. See Sambuca Jacket in Amazing Crochet Lace by Doris Chan.
If anyone has historical information on the "Picot Fans" stitch pattern, please let me know. I suspect someone modified a scalloped edging pattern.