Why is it a Color “Wheel” and Not a Color “Line”?

This blog post was published in May of 2012 on EyeMath. It is being migrated to this blog, with a few minor changes.

I’ve been discussing color algorithms recently with a colleague at Visual Music Systems.

We’ve been talking about the hue-saturation-value model, which represents color in a more intuitive way for artists and designers than the red-green-blue model. The “hue” component is easily explained in terms of a color wheel.

Ever since I learned about the color wheel in art class as a young boy, I had been under the impression that the colors are cyclical; periodic. In other words, as you move through the color series, it repeats itself: red, orange, yellow, green, blue, violet…and then back to red. You may be thinking, yes of course…that’s how colors work. But now I have a question…


Consider five domains that can be used as the basis for inventing a color theory:

(1) the physics of light, (2) the human retina, (3) the human brain, (4) the nature of pigment and paint, and (5) visual communication and cultural conventions.

(1) In terms of light physics, the electromagnetic spectrum has a band visible to the human eye with violet at one end and red at the other. Beyond violet is ultraviolet, and beyond red is infrared. Once you pass out of the visible spectrum, there aint no comin’ back. There are no wheels in the electromagnetic spectrum.

(2) In terms of the human retina, our eyes can detect various wavelengths of light. It appears that our color vision system incorporates two schemes: (1) trichromatic (red-green-blue), and (2) the opponent process (red vs. green, blue vs. yellow, black vs. white). I don’t see anything that would lead me to believe that the retina “understands” colors in a periodic fashion, as represented in a color wheel. However, it may be that the retina “encourages” this model to be invented in the human brain…

(3) In terms of the brain, our internal representations of color don’t appear to be based on the one-dimensional electromagnetic spectrum. Other factors are more likely to have influence, such as the physiology of the retina, and the way pigments can be physically mixed together (a human activity dating back thousands of years).

(4) Pigment and paint are very physical materials that we manipulate (using subtractive color), thereby constituting a strong influence on how we think about and categorize color.

(5) Finally: visual communication and culture. This is the domain in which the color wheel was invented, with encouragement from the mixing properties of pigment, the physiology of the retina, and the mathematical processes that are formulated in our brains. (I should mention another influence: technology…such as computergraphical displays).


Consider the red-green-blue model, which defines a 3D color space – often represented as a cube. This is a common form of the additive color model. Within the volume of the cube, one can trace a circle, or a hexagon, or any other cyclical path one wishes to draw. This cyclical path defines a periodic color representation (a color wheel). A volume yields 2D shapes, traced onto planes that slice through the volume. It’s a process of reducing dimensions.

But the electromagnet spectrum is ONE-DIMENSIONAL. The physical basis for colored light cannot yield a higher-dimensional color space. The red-green-blue model (or any multi-dimensional space) therefore could not originate from the physics of light.


An alternate theory as to the origin of the color wheel is this: the color wheel was created by taking the two ends of the visible spectrum and connecting them to form a loop (and adding some purple to form a connective link). I just learned that Purple is NOT a spectral color (although “violet” is :) Purple can only be made by combining red and blue. Here’s an explanation by Deron Meranda, in a piece called…


And here’s a page about how purple is constructed in the retina: HOW CAN PURPLE EXIST?

Did the human mind and human society impose circularity onto the color spectrum in order to contain it? Was this encouraged by the physiology of our eyes, in which various wavelengths are perceived, and mixed (mapping from a one-dimensional color space to a higher-dimensional color space)? Or might it be more a matter of the influence of pigments, and the age-old technology of mixing paints?

Might the color wheel be a metaphorical blend between the color spectrum and the mixing behavior of pigment?

Similar questions can be applied to many mathematical concepts that we take for granted. We understand number and dimensionality because of the ways our bodies, and their senses, map reality to internal representations. And this ultimately influences culture and language, and the ways we discuss things…like color…which influences the algorithms we design.



3 thoughts on “Why is it a Color “Wheel” and Not a Color “Line”?

  1. Why is it a Color “Wheel” and Not a Color “Line”? | Eye Math

  2. The wheel and the line define the color spectrum from two completely different postulates depending on the intended purpose. I saw both of these representations as a kid and understood them to be just that; one defining the breakdown of light by frequency and one to illustrate the relative nature of mixing paints to shift color values in the plastic arts. Why do globes and
    maps always orient north?


    I would say it’s more like humans already had purple and needed a place to glue it, and I’d also say that the answer kind of depends on all 5 of the domains you listed.

    Each of the individual wavelengths of visible light will have at most 2 primary cones that it activates, because the wavelength will either be “at” a single cone, or will be “between” either the red and green cones or the green and blue cones (roughly).

    Now, all of the activation patterns that you got at each wavelength can be recreated by mixing primary RGB colors, where the colors are limited to being either mixtures of R and G, or mixtures of G and B (including combinations that use just one of the colors). To simulate a wavelength that activates R and G equally you just use equal portions R and G. The retina will have the same activation pattern in response to either stimulus, and the same activation pattern leads to the same perception.

    Being able to perceive gradients and contrasts aids in the perception of things as being connected or disconnected, which leads to useful visual pattern-recognition (all the moreso since color is directly connected to physical composition). Two points of light that generate almost the same activation pattern are likely to be coming from the same physical object. This will hold true across the space of all activation patterns, and each activation pattern corresponds to a color, so if two activation patterns are close together, then their corresponding colors are perceived to be close together or even “connected” as well, so it does make sense that the perceived structure of color would have a basis in the smooth gradient line of the visible spectrum.

    Now, if we have all cones activated equally, then we have no color. If they’re activated fully we get white, if they’re not activated we black, and in between we have shades of gray. Any uneven activation of the cones is to be interpreted as a color. The only activation pattern we haven’t covered yet is R and B, which of course gives rise to purple. No wavelength in the rainbow activated both of these cones at the same time, and thus we see no purple in the rainbow, but we can still make the R and B activation pattern happen by mixing red wavelengths and blue wavelengths. The brain doesn’t know anything about wavelengths, all it knows is that we’ve got an R+B activation pattern. But the same evolutionary logic will still hold true that a smooth-gradient of R+B activation patterns will likely part of the same object. Further, R+B activation patterns can be seen as being *physically* between red and blue, in the sense that they come from objects that contain molecules emitting/reflecting both red wavelengths and blue wavelengths. “If those violet berries poisoned me then these slightly reddish violet berries that look exactly the same might poison me too” etc..

    So I think that pretty much explains why there would be some color purple “in between” red and blue, thus connecting the end-points of the linear visible spectrum to form “at least” a color wheel. “At least” because now we might wonder why we don’t tend to perceive color as going in like.. a sphere, or figure-8, or some other more complex structure that simply contains the color wheel?

    It seems part of the reason we’re restricted to two-dimensionality and simple shape is because of the limited number of different types of cones: if you have three points you can connect them in a triangle but you don’t have a fourth point to maybe be extending into a higher dimension (maybe some animals with 4 cones can see a color-sphere?). You also don’t have any lines crossing, etc.. So we might assume our basic model is a color triangle where the points correspond to cones / primary RGB colors and the lines correspond to secondary RGB colors / simultaneous activation of “adjacent” cones (adjacent on the triangle).

    We can even start to reconstruct a notion of “opposite” colors from this: we can speak of the line that’s opposite to a point on the triangle, or in this case the secondary color that’s opposite to, or “complementary” to, a primary color. Interestingly this seems to be almost exactly what the retina/brain already does: the true/RGB-complement of red is cyan which corresponds to the green and blue cones being roughly evenly activated, and we see cyan opposite to red on a true/RGB color-wheel (as opposed to the standard art-class RYB color-wheel). These opposite/complementary colors really do seem “opposite” to us: it’s not the same smooth rainbow gradient like between adjacent primary colors, they are as sharply contrasting as possible when separate, and create earth-tones “inside the wheel” when combined. Note that none of these earth-tones are in the visible spectrum either. Did we invent them in order to connect opposite points of the color-wheel together?

    So.. why would colors have “opposites”? The answer seems to be about contrast. Based on the evolutionary logic applied above, we would want to be able to use color for perception of both gradient and contrast, so some colors have to be contrasting. This doesn’t explain why colors would seem to come in complementary pairs on opposite sides of a circle/disk though. However, there does seem to be an explanation for this in terms of biology. The human brain appears to piggyback its perception of oppositeness of colors off of similar mechanics to its perception of the oppositeness of black & white. The complement of a color is the color such that when they’re combined, all cones are fully activated. For every different activation pattern of the cones, there is a unique opposite/complementary activation pattern such that their sum is the activation pattern corresponding to white. So black appears in high contrast to white because the sum of black and white is all cones fully activated; red appears in high contrast to cyan because the sum of red and cyan is all cones fully activated. If you combine them in uneven amounts, you get an earth-tone spectrum unique to that complementary pair. Going with the notion that the mind is separating complementary colors in the same way that it separates white from black, then these earth-tone spectrums would each be a color-equivalent of a gray-scale. This seems to partially explain why we perceive the rainbow colors + purple as being somehow more “colorful” than earth-tones. Further evidence for this notion can be found with the perception of warm colors (red orange and yellow) vs. cool colors (cyan blue and violet). They are complementary to each other, and warm colors are generally perceived to be associated with light and cool colors with dark. Even more convincing is the biological mechanism for the perception of “after-images”. Also check out Goethe’s work with prisms and contrast.

    Since all of this same logic can be applied to any cone activation pattern, the perceived structure of the color-space doesn’t need to distinguish the points on the color triangle/lines associated to the primary cone colors and their complements, and so we can make our model rotationally invariant, turning our color triangle into the complete and standard color wheel where the 3 primary and 3 secondary colors from the triangle just appear as the main 6 recognizably distinct sections of the wheel: red, yellow, green, cyan, blue, & magenta/purple.

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