Thinking out loud about designs for a POV “flow wand” (http://www.flowtoys.com/product.php?productid=2).
Using LPD8802 strips mounted on a cardboard triangular prism, housed inside a translucent polycarbonate tube with 15mm wide strips, you’re looking at a minimum tube inner diameter of ~18mm (though that handily does allow me to fit an 18650 at each end for power.)
But at 18+mm outer diameter, that’s starting to look much more like a staff than a wand. The APA104 strips are 10mm wide, for an inner diameter of 12mm (fitting 10440/AAA cells), but then I’m out of space for the controlling 'duino.
Even narrower, I could dead-bug a bunch of PTH WS2812 (https://www.sparkfun.com/products/12986 —or LPD8806, if they exist?) together and run them into ~6mm ID tube, but at that point I’m out of options for batteries too.
I would LOVE to use the RFduino/RFD2201 module (http://www.rfduino.com/product/rfd22301-rfduino-ble-smt/) for this, and do all the control/pattern uploads from an iPhone app as that frees me from having physical switches on the device and allows me to coordinate pattern switching across multiple wands. But these are still 15mm across their narrowest dimension.
Anyone know of a production Arduino (BTLE or not) that’s narrower than 15mm on its smallest side?