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I had a vision of a creature that touched things, and wherever it touched, it left a mark opposite to the original colour.
For example when it walked across the grass the grass had red footprints, when it touched the wet stone it shone with a patch of white.
Could such a material, a liquid or perhaps a dust, that achieves the described effect exist?
If yes, how might it work or what would it be made of?
No, not directly
The nature of light means that you can't just shift its colour so easily. Each colour is create by a particular wavelength which has an associated energy. There are ways that the wavelength can be changed, but they are limited. Two photos can be combined to make a single photon of twice the energy (this is how most green lasers work), but since the energy of the shortest wavelength of visible light is just under twice the energy of the longest wavelength, this may not be preformed on any light in the visible spectrum and still get another visible wavelength. Fluorescence can absorb one frequency of light and emit another, but typically the emitted light is of lower energy (there is some higher energy light emitted as well).
The next problem is that "opposite" colours only occur due to how the brain reads light signals. The colour spectrum is linear, red->green->blue, purple does not exist, it is simply our interpretation of seeing red and blue at the same time. Opposite colours depend on a circular interpretation of colours that conflicts with the fundamental nature of light.
Now if you want such a creature to exist, you can, but the results must be obtained indirectly. The first option to do this is have the creature excrete multiple chemicals, and purposely select them based on their surroundings. The second option is to identify that a large amount of colour comes from a limited amount of pigments (chlorophyl, iron oxides, copper oxides). If the creature carried a compound that formed various pigments in reaction to the more common pigments it comes in contact with, it could effectively change their colours. This second option would be hard to implement, as each pigment changing chemical would have to avoid reacting the the other pigment changing chemicals.
Twenty-five years ago I had a friend in the military who told me about glasses he was issued that used passive technology (layers of various materials) to shift the frequency of light, allowing the user to see images at a base frequency that wasn't the original frequency (everything shifted toward the blue frequency, as I recall). For all I know he was explaining a tech he didn't fully understand. However, that's as close as I can imagine to what you're asking about.
Inverting frequencies is, IMO, impossible. I could be wrong, but it means you need a layer that passes blue light but shifts red to blue, and then another layer that passes red light but shifts blue to red.
And you already have an impossibility, because the effect of the first filter will always be reversed by the second filter. There's no way to tell the second filter, "here's unfiltered light, don't touch the stuff I've already dealt with."
To add to the problem, "color" is actually a range of frequencies. You're not "inverting" the color, you're shifting the wavelength (frequencies) up and down. Except that the "inversion" of a color may shift up for one color and down for another and that might not be passively predictable. In other words, everything doesn't simply shift down.
Conclusion
There isn't and cannot be a passive system that "inverts" color. The inversion of a color is not mathematically objective and when you bring multiple layers of materials into play, lower levels of filters will undo what the upper filters did.
You can only do this with an active system. AKA, a camera-computer-screen solution that detects the colors and inverts them for display on the screen in real time.
One more thing, this is one of those, "if I had the answer, I wouldn't post it here, I'd be running to the patent office" questions. I can most certainly be wrong. I don't know everything about material science, optics, and color shifting. But I also don't know of anything on the market that can do this — or even what I described from my old friend. Therefore, it's reasonable to believe that such a valuable invention wouldn't be posted here.
Color perception is a physiologic phenomena: we see red as the negative of green because we have a particular mechanism in our eyes in which certain wavelengths and not others interact with the receptors.
For a dog or a bee it would be different.
Therefore, if you want to alter the physiologic perception of color, you might go for a fictional psychedelic substance which, instead of causing synesthesia, messes up with the neurons elaborating signals from the optical nerve.
I think a lot about this. Specifically, a substance that changes color based on the light rays entering it. In this case, it will be harder, but still doable. Here we go.
Start off with a protein suspended in a liquid. This liquid is secreted by your creature constantly in a very thin film. The protein is activated by light, specifically by the light bouncing off something. When light of a certain strength, or wavelength, hits it, it distorts the protein and causes it to fold differently. This folding takes it to the opposite end of the spectrum from the light originally hitting it, and so the light that bounces off it is inverted. Simple, except for this protein that probably would be very hard to make. But oh well, that's the burden of world building. If the protein concentration is high, you can get away with a very thin film of liquid, just covering a touched surface.
I think that a lot of people were getting messed up by the way we experience artificial color- specifically as RGB/CYMK/XKCD/whatever color acronym you want. In reality, it is just wavelength.
Yeah, that. The shorter the wavelength, the higher the energy, the more the colors go in the opposite direction towards the infrared spectrum. In short, this could work, but it might be a bit weighty for readers. Have fun!
How about the creature leaves a protein that reacts with the color of the surface, and changes color based on that, with the color happening to be the inverse?
This solves the most fundamental problem of "no single known material" to do this, while also skipping the handwavium. There are certain seaslugs that leave brightly-colored residue, so a slime made up of one color-changing protein that reacts differently to different surfaces or many proteins where only one of the set reacts to each color should get you by.
Alternatively, you could use one or several highly unstable protein(s) that reacts very quickly to reflected light, changing color via denaturing very quickly based on the heat absorbed from the material it is on.
EDIT: For reference, here's a few:
This is a purple one with purple slime (it's also giant):
This is a blue dragon slug when it's not in the water, and slime has the opportunity to accumulate:
Here's normal for reference:
By mechanism, there unfortunately aren't any of their slime trails while in the water (since it just gets washed away), but barring that they are just colorful slugs with colorful slime.
Hope this helps!
Color is a perception, so to hit the polar opposite on the color space (you specified that not only color, but also luminosity gets inverted) the creature needs to have evolved in reaction to human (or whatever perceiving entity) color perception, or the effect is just the damnedest luck (or it is just an approximation and gets embellished in the retelling?).
The creature is able to camouflage itself perfectly (towards a given species of predator). Towards this goal, it has a broad range of chromatophors, basically squishy sacs of pigment that can be muscularily manipulated to present more or less of themselves on the skin's surface, and crude eyes all over it's body's surface.
When moving, the creature constantly, autonomously, replicates any color it senses on one side towards the other side, so a bit more advanced than an octopus. For communication purposes, or mimicry, it can also detach it's color production from the input by the other side's eyes, it can, for convenient instance, produce the polar opposite of any point in color space, for maximum visibility. As an added trick, it can slightly open the chromatophores, releasing a measured portion of pigment, to create 'afterimages', either for fooling a predator or communication.
It is not used to either dry land, or oxidised surfaces, or something else unique to your setting, thus the chromatophores spring a leak whenever it touches anything. Additionally, the touch sensation triggers the touching part of the skin to display the polar opposite of the last colors seen before touching. It thus leaves a print as you specified.
Adding to the good answers, if inverted black is white and inverted green is red, you're doing two things: inverting brightness, and inverting hue, which is rotating the color circle 180°.
I'm not sure how you could invert brightness physically, but it's the easiest one. You couldn't create brightness, but you could absorb light when the material reflects and reflect when the material absorbs.
However, "rotating on the circle" is something else. That circle is purely based on how human eyes work, and wavelength don't work in a circular pattern, they're absolutely linear. You'd need to shift the wavelength up (or down), except when it reaches out of the (human) visible light spectrum, report by how much the wavelength was shifted on the other side of the spectrum.
Like JBH said, it's doable with an active system but not a passive one.
Not sure why others say it can't be. For instance, you can make a a filter which filters out blue light and behind it one which shifts red to blue or whatever you like (depending on whether you mean opposite colors on the spectrum, complimentary colors for our eyes or something else). Besides it, you make one which filters out red light followed by one which shifts blue to red. With a little bit of leakage, the middle frequencies (yellow and green) also get switched around.
This will lose you 50% of the light, but switch colors.
If you added polarisation tricks, you might actually be able to reduce the loss of luminescence to some degree...
It's going to be difficult to make a material that inverts colors when you look through it, however your hypothetical creature does not need to do this. The easiest way I can think of to do this would be that the 'paint' the creature leaves contains special chromatophores or color changing cells. The chromatophores are initially excreted clear, they then sense the color of the object underneath and then suddenly transition to the opposite color, this is necessary because they will modify the light going through to the surface and may get confused if the change is slower. As animal chromatophores work by modifying their reflective properties, going from dark to white should certainly be possible.
Easily possible. I think I can describe a passive system that could accomplish this.
But first: Tut, tut. Inverted footprints on grass would be magenta (purplish), not red! Color theory matters!
Consider the three following hypothetical fluorescent substances:
[These are the "opposite" colors for the typical human eye, as a matter of basic biology (not physics!). Learn them, love them, and mock the crap out of any art teacher who tries to teach otherwise.]
Each of these absorb and fluoresce over a range, not just a specific frequency (pair of frequencies, for magenta), carefully chosen to match the human eye.
Each of the substances take the light on one side, and shine it out the other side. So if they are on a green leaf, and white sunlight comes in, they absorb RGB white light, and shine CMY white light down onto the leaf. The leaf reflects mostly green (from the yellow + cyan overlap), which is absorbed only by the magenta-emitting material.
The overall effect is that, when these three materials together are sprayed on a green thing, it glows magenta.
This gets you the color-wheel hue-flipping fairly easily, without needing any kind of context-sensitive chemicals.
Tetrachromats, the colorblind and others will not really see the illusion correctly, but then, they won't see it correctly however you flip it. Their eyes work differently, they don't have the same primary colors.
There's still the problem that the brightness needs flipping too.
Since the above relies on a light-path through the three filters to the leaf and back again, we have made this task much simpler, as if it flips indiscriminately, it will flip from light to dark and back, as the light goes through and back.
But what if the metamaterial polarizes itself? The particles are charged. They align by consensus: each particle aligns to the average of its neighbors. Rapidly, pockets of similarity emerge, and the whole pool snaps to a single polarization, like throwing a handful of small magnet-beads into a bowl.
Now each particle blocks all "vertically-polarized" light (where "vertical" is defined as whatever average alignment the particles locally have agreed to align with).
And each one rotates the polarity of the light going through it by an angle from zero to 45 degrees, depending on the intensity of the light it is absorbing.
At the brightest light, light enters the filter layer, is flipped to its inverse color and rotated 45 degrees, is reflected back, flipped 45 degrees again, and so has been rotated 90 degrees and does not get through.
In the dimmest light, it gets rotated zero degrees coming in, and zero again on the return path.
That takes care of it darkening in bright light.
But what about glowing in dark light?
Well, that's the speciality of fluorescence!
Personally, I'd just skip the "darkening in bright light" thing (it's not part of the spec, explicitly, except that white should probably turn dark. Screw that, just have white turn WHITER!).
Instead, let's have our three original substances all also absorb non-visible wavelengths like UV and IR, and fluoresce them at their chosen output wavelengths.
Then the footsteps will always glow the opposite hue:
To find which color you'd see, go to your favorite image editor (or image editing website), invert the hue (Shadows and highlights should not flip, only the hue!), then increase the brightness a little.
There are at least four physics processes that alter the frequency or color of photons.
In Scintillation higher frequency (energy) photons thermalize electrons which remit the light at a lower frequency (energy). Scintillation could account for blues becoming reds
The Zeeman and Stark Effects both cause optical modulation and result in spectrums spreading out. Conceptually, this could cause reds to go to blues but these effects are typically more subtle. I think they could explain dark greens going light and vice versa
The last process in my list of four is absorption-remission. If excitons (excited charge carriers) are trapped in a meta-stable state they can only transit out of the excited state by phonon emission. But, if these trapped excitons absorb enough energy to reach a band in the molecules conduction band, they can transit back to the valence state by emission of a photon. HeNe lasers operate on this principle. If the difference between the meta-stable state and a conduction band is equivalent to red photons, and the difference between conduction and valence bands is equivalent to blue photons, then this would be perceived at a red to blue transformation.
All of these processes except scintillation depend on magnetic (Zeeman Effect) and electric fields (Stark Effect) or an energy source pumping the electrons to meta-stable states (absorption-remission) so they wouldn't really be considered passive. But, conceptually, you are dealing with slime or goo from a creature so its chemical breakdown could be providing energy that powers these transformations.
