I sort of wonder is there a "true" way to represent color? Would a intensity over frequency curve do it?

I probably lack the terminology to express myself properly, but color ends up being a very human thing, with a huge focus on primary colors(the colors that match the frequency response of the human eye) This is fine, we are human after all, but then I always feel color theory dives off the deep end, with color wheels and complimentary colors and triplets, etc. why? there is nothing physically cyclic going on. It never makes any sense to me that patterns based on it being cyclic would be any better than just picking colors. Any way, silly rant aside, if we wanted to define an objective physical color format, how would it be done?

> I sort of wonder is there a "true" way to represent color? Would an intensity over frequency curve do it?

There’s no single “true” way because color isn’t a fixed property of light itself, it’s the result of how a visual system interprets wavelengths.

Having said that, if you’re looking for an objective way that doesn’t depend on observer, you could use spectral power distribution.

That would be the mix of wavelengths present, plotted as intensity vs. wavelength.

That’s because a single wavelength (say 580nm) produces one specific color sensation, but many different combinations of wavelengths can produce that identical sensation (called metamers), so representing color by wavelength alone isn’t even uniquely “true” perceptually.

You could go a long way by specifying the reflectiveness over the visible light spectrum and then do the same for light sources. That way, you could do GDR style truly monochrome sodium vapor lamps, which makes telling colors apart impossible.

To do neon colors, you would need some sort of frequency redirect in your texture data as in "this pixel absorbs 80% infrared, but reemits it as visible red". Then you could have black light light sources and cool poster textures as well.

I think doing textures in this format would take too much space, but doing a 256 color palette that way might be fine.

> there is nothing physically cyclic going on

If you plot the three primary colors with all possible combinations of only two of them, you can connect them all neatly using a circle, and distance on that circle does tell us something about how visually distinct colors are. It isn't much more profound than that.

One of the colors on the circle, magenta, has no corresponding pure wavelength, because in order to see magenta, your red and blue cones must be activated, but not the green cones -- you need two frequency peaks to do this. If we had four different types of cones, like many birds, there would be many more non-spectral fully saturated colors and you'd need something like a hypercube to represent them.

> Would a intensity over frequency curve do it?

That should work as a brute-force method. You could simulate lighting conditions by measuring the reflected spectrum of different materials and multiplying with the spectrum of a light source.

Check out the CIE XYZ color space and its color matching functions. It's the standard for defining/converting color spaces and calibrating displays for accurate color matching. It only models human perception, and contains colors that are physically impossible to reproduce.

https://en.wikipedia.org/wiki/CIE_1931_color_space

The term you're looking for is "color space".

Depending on what you want to do there's CIE XYZ (maps spectrum of color to a 3 component vector by integrating the spectrum multiplied by three functions), CIE Lab* (describes the color of objects under a specified illuminant), CIE Luv* (to characterize emissive source, nonlinear so the the distance between colors corresponds to perceived differences).

These color spaces are built to objectively describe colors, as seen by a human with typical color vision.

Colors only exist in the human brain, they're qualia, interpreted from the mixture of wavelengths our eyes detect.

“I’ve thought about this for five minutes, and it seems so simple. It must be the tens of thousands of vision scientists and psychophysicists who have worked on this for the last century who have all missed how simple it is.”