Visualizing Color Interactions

I was trying to understand something about color. I know that red, green, and blue light sources can be combined to make white light. And I understand that cyan, magenta, and yellow inks can be combined on the page to make a black (or near black) ink.

But…you can get cyan, magenta and yellow light sources. And you can get red, green and blue ink. What happens if you combine those? It didn’t make sense that combining three light sources would make black, or that combining ink would make white. What was going on?
I knew the solution had something to do with the difference between additive color and subtractive color, but I had to sit down and work it out to get my head around it. In the process, I figured out a notation system to describe and visualize color interactions that I want to share with you.
It’s easiest to start with the subtractive colors. The reason we call them subtractive, of course, is that they remove colors from light. When white light falls on red ink, the ink absorbs all colors except red. This is what is reflected back to our eyes, and therefore we see red.

The same is true of any color—even the CMY colors. In fact, cyan, magenta and yellow are each exact counterparts to red, green, and blue: cyan absorbs all red from white light and reflects everything else. Similarly, magenta absorbs all green, and yellow absorbs all blue. (In theory, anyway—the truth is that no ink absorbs color perfectly, so we never see ‘pure’ cyan on the page.)
Thus we could alternately name cyan anti-red, because it removes red. For simplicity, we can notate this as -R. Likewise, magenta is anti-green, or -G and yellow is anti-blue or -B.

Where this gets interesting is when we combine these notations: cyan and yellow together—or anti-red (-R) and anti-blue (-B)—become anti-red-blue: -RB. If white light is an equal combination of red, green and blue, then anti-red-blue absorbs both red and blue, leaving…green.

RGB + (-RB) = G

Cyan, Magenta and Yellow as Anti-Red, Anti-Green and Anti-Blue
Cyan, Magenta and Yellow as Anti-Red, Anti-Green and Anti-Blue

If you assign hard numbers to this equation, it makes perfect sense. Using hexadecimal color numbers, we get:

FFFFFF - FF00FF = 00FF00

You can make up similar equations for the other anti-colors. Most importantly, if you combine all three, you get -RGB, better known as black.
But what about my original question? What if you use red, green and blue ink? What happens when you combine them? Note that we now have another set of names for them: red is now anti-green-blue, green is anti-red-blue and blue is anti-red-green. The notations would be: -GB, -RB, -RG. Combining them tells us what happens when we combine them on the page:

(-GB) + (-RG) = -R2GB

Red, Green and Blue as Subtractive Colors
Red, Green and Blue as Subtractive Colors

The -2G is unusual: it’s saying, in effect, “absorb twice as much green as there is in the white light”. Of course, actual ink can’t do this, anymore than you can empty 10 liters out of a 5 liter bucket. In practical terms, this just means you’ll have a pigment that looks black, but has a slight magenta (i.e. anti-green) cast to it.
Red, green and blue ink also combine to make (-RG) + (-GB) + (-RB) = -2R2G2B. It’s still black: all three components are equal. But the doubling still holds.
Subtractive colors work by absorbing color from light that falls on it and reflecting only a portion of the light’s spectrum, such as light falling on colored paper. They apply when dealing with reflective surfaces that don’t produce light on their own. By contrast, we use additive colors when dealing with emissive objects: things that emit light, like a light bulb.

We can use a variant of our notation to explain what happens when combining emissive light sources. In this case, since we’re working with additive colors, we count each as a combination of red, green and blue: cyan is +GB, magenta is +RB, and yellow is +RG. This is because instead of subtracting light, we’re adding it. Thus, whereas subtractive cyan is -R, additive cyan is +GB, a combination of green and blue.
You can see how red, green and blue work as additive colors. By combining them, we can also get cyan, magenta and yellow.

The standard additive colors red, green, and blue
The standard additive colors red, green, and blue

This is probably familiar: most textbooks on color cover combining red, green, and blue light sources. But just as we can have red, green, and blue ink (i.e. reflective surfaces), we can have cyan, magenta and yellow light sources (i.e. emissive objects). The reason they aren’t commonly used is that, just like with RGB inks, CMY light sources aren’t as flexible, and our notation helps us see why.

When we overlap these sources, we again get some doublings: if cyan (+GB) overlaps with yellow (+RG), we get +R2GB, light with ’double’ the amount of green compared to red or blue.

The bucket analogy still holds, in reverse: you can’t pour 10 liters into a 5 liter bucket, either…at least not without a lot of spillover! There will be more green light in this case than red or blue. So in reality, we get a white with a greenish tint.

Cyan, Magenta and Yellow as Additive Colors
Cyan, Magenta and Yellow as Additive Colors

Pure white, of course, can be made by combining cyan, magenta and yellow: (+GB) + (+RB) + (+RG) = +2R2G2B. Again the doubling comes into play.
Color is a fascinating subject (even if it gives some people headaches). Working this out helped me understand why printers and screens use different primary colors, and appreciate the cleverness of this technique.

It turns out even using simple colors is a colorful subject.

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