>this case they're not directly using the color to store information, they just have three differently colored QR codes overlayed on top of each other. With that method you can use a filter to separate them back out and you've got three separate QR codes worth of data in one place. The way they're added ends up using more than just three colors in that example.
That's only true if you can print and read colors in a higher resolution/don't destroy information at 3x the density with color, I'm not sure if that's generally true.
>If you were truly to use colored dots to store binary information without worrying about using a standard like QR, I think you'd be going from base-2 (white and black) to base-3 (red, blue, green) or more likely base-4 (white, red, blue, green) or even base-8 (if you were willing to add multiple colors on top of each other) in which case yeah you'd have way more than just 3x the data density.
Base 8 is exactly 3x the data density. (Log(8)/log(2))