Look at these 1880's stitch drawings. I'd never seen the "eye" part of the star accentuated like this (the chain-1 that completes each star forms the "eye"). I didn't realize the one on the left is also a star stitch until I swatched it (light blue swatch just below).

Accentuating the Eyes vs. the Spokes
 

It turns out that how you pull up the loops to form the "spokes" of the star can make them look more like petals around a flower center.
 Plum swatch at left is one of the more petal-like variations I tried (I added yarn-overs before pulling up some of the loops).

A 1891 drawing (see third drawing at right) kept coming to mind after I finished Starwirbel. The Star stitch eyes are big and open in Starwirbel, but in this drawing, the eyes are "closed." All you see of these stars are the "spokes."
 

I swatched it in light fingering weight Danish wool with a 6.5 mm ("K") hook. It looked like the drawing until I blocked it.

 Starry Eyes: Closed or Wide Open?
 

How do you get starry eyes to open or close? One key factor is how many loops are pulled up in the eye. Use a bigger hook and crochet more loops in the eye to hold the eye open wider. Makes sense, doesn't it? For closed eyes, one thing you can do is skip working into the eyes entirely.

Rows (Turning) vs. Rounds - In other words, must all rows face the front? Some of the best-known star patterns require cutting the yarn at the end of every row. You can also turn and do a non-star row, such as all single crochets in the eyes only, or not. With lacy stars, choosing one of these options can create a whole new look!
 

Weird, Wonderful Lace Weight Yarns

Playing with yarns from the Lace Weight category is an adventure: I'm swatching stars with primarily wool types - not cotton crochet threads. It's a weird catch-all type of yarn category. Crochet thread sizes overlap with it, and are more precise than superfine yarn sizes. See how different the star stitches look in these three lace weight yarns? All were crocheted with the same 6.5 mm ("K") hook:

(L to r: fine micron merino; cashmere; baby alpaca.)

Yarn choice has a dramatic influence. Loopy loose-gauge stars are quite the divas: just a sprinkle of sequins or metallics lights them up! Alpaca and mohair make loops spring open or look coiled. A tightly spun yarn does too. I wrote an early newsletter issue about this: "Fibers that Sproing" (2011): http://eepurl.com/cwHt9).