Function one shows a single pixel traveling up the LED strip.
The Real Quick Runner goes quite a bit faster.
Below shows the four pixel fading trail. From the code you can see I just needed to change:
int pos = beatsin16(10, 0, NUM_LEDS);
the ten as the first argument to an 8 to create a 3 pixel fade.
Midway the LED switches colors from purple to blue.
HSV dimming trail of changing colors
I had a lot of trouble simply getting the LED strip to not be finicky. I used two 330 resistors for the data and clock pins but found that the slightest movements on the table or even a door banging shut would render my pixels frozen. I ended up jamming some extra jumpers to hold the resistors still. I also had to solder the strip connections twice because the jumpers would fall from the carefully soldered ports.