I started with a purchased summer hat with a stiff enough brim to hold electronics. I created multicolored flowers out of sheer fabric, with an Adafruit NeoPixel at the center of each one, controlled by an Adafruit GEMMA microcontroller board and powered with a small lithium polymer battery. This battery will power the hat for many days; I'm not actually sure how many, since I haven't let it run until the battery runs out.
The GEMMA runs a bit of code that smoothly changes the NeoPixel colors in a continuous loop. Here's a video (playable in most modern browsers) that shows this in action: