You do this: Connect some sort of circuitary to the single pin, then use some software to switch it on and off in a sequence dpendant on the colour required (more on this below). Data transmission rates could be slow, but then it's only going to change once every few seconds anyway.
To send the signal, you could do something like this:
-We need six colours
-To encode this we need 4 bits
-To send this we switch the signal on and off like in a serial cable.
So, for example, to display orange (colour 3 in the logo), you would send: 1 start bit, 4 data bits: 0011, 1 stop bit. (Actually, you could even drop the stop bit.) Then you just need some sort of circuit to decode that. A slow rate of even something like 2 bits per second would be enough.
Or, alternatively, you could just send a single pulse, and have the hardware remember what colour it's displaying, and thus decide on the next one.
Or, even better (sorry, I had a brain surge), you could (although this would need a higher bps rate and possibly a microcontroller at the other end) even send something like 4 or even 8 bits for each colour, so something like this: 1 start bit, 8 data bits for DAC conversion to Red component, 8 data bits for DAC conversion to Green component, 8 data bits for DAC conversion to Blue component, 1.5 stop bits. (It would be advisable to include an easily recognisable stop bit signal, otherwise the system might hang waiting for a missed signal.)