Finally I programmed some patterns for the NeoPixel rings.
Unfortunately the colours are not as bright as in real life.
The description of the patterns is below:
windmill: a windmill-like pattern. The colour changes with every step in the HSB circle.
blinkwhite: some LEDs are blinking. Thanks to Balász Suhajda for the sketch.
blinkcol: like above, only with colours instead of white.
christmas: red and green blinking LEDs.
fill: fills the rings from outer to inner rings with a random colour.
random1: set every LED toa random color.
The complete source code is on github.