Pictures are
here.
Notation: By "ch 3 w/b" I mean "chain three with a bead", that is, ch 1, ch 1 with a bead, ch 1. Similarly, "ch 5 w/b"
is ch 2, ch 1 with a bead, ch 2.
"bp" means "bead picot": Ch 1, ch 1 with a bead, sl st in 2nd ch from hook.
Stitches to be worked into the same stitch or chain loop are enclosed in (parentheses). Stitches to be repeated are surrounded by *asterisks*; a #numbersign indicates that you are to stop there on the last repeat. So, for example,
"*2 sc, #ch 3* 6 times" would mean to make 12 sc and 5 ch-3 loops.
Ariel's Snowflake, Version 1
Ch 6; join with a sl st to form a ring.
Round 1: Ch 10, *2 dc in ring, ch 7* 5 times, dc in ring, sl st in third st of ch-10 loop. (6 loops.)
Round 2: Ch 1, *sc in first 3 chs of ch-7 lp, (sc, ch 5, sc) in next ch, sc in next 3 chs of ch-7 lp, #sc in next 2 dc* 6 times,
sc in next dc, sl st in initial ch.
Round 3: Ch 3, *(dc, ch 3 w/b, dc, ch 5 w/b, dc, ch 3 w/b, dc) in ch-5 lp, sk 4 sc, dc in next sc, ch 3 w/b, #dc in next sc* 6 times, sl st in top of ch-3.
Ariel's Snowflake, Version 2
Ch 9; join with a sl st to form a ring.
Round 1: Ch 9, *3 dc in ring, ch 6* 5 times, 2 dc in ring, sl st in third ch of ch-9 loop. (6 loops.)
Round 2: Ch 1, *sc in first 3 chs of ch-6 lp, ch 2, sc in next 3 chs of ch-6 lp, #sc in next 3 dc* 6 times,
sc in next 2 dc, sl st in initial ch, sl in last sc made.
Round 3: Ch 2, *(dc, ch 3 w/b, dc, ch 5 w/b, dc, ch 3 w/b, dc) in ch-2 lp, ch 1, sk 4 sc, sc in next sc, ch 3 w/b, #sc in same sc* 6 times, sl st in first ch of initial ch-2.
Ariel's Snowflake, Version 3
(Note that I haven't actually tried this one yet!)
Ch 9; join with a sl st to form a ring.
Round 1: Ch 3, dc in ring, *ch 5, 3 dc in ring,* 5 times, ch 5, dc in ring, sl st in top of ch-3. (6 loops.)
Round 2: Ch 1, sc in next dc, *3 sc in ch-5 lp, ch 7, sl st in 6th ch from hk, ch 1, 3 sc in ch-5 lp, #sc in next 3 dc* 6 times,
sc in next dc, sl st in initial ch.
Round 3: Ch 3, *(dc, ch 1, bp, ch 1, dc, ch 2, bp, ch 2, dc, ch 1, bp, ch 1, dc) in ch-5 lp, sk 4 sc, dc in next sc, bp, #dc in same sc* 6 times, sl st in last ch of initial ch-3.