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In my world there exists a sort of "chameleon" like cloak that has the ability to change its color to blend in with its surroundings, the fabric is thus highly sought after for its camouflage capabilities.

So I am looking for a way to justify/explain this cloak's "camouflage/chameleon" capabilities.

Ideally a semi-plausible science-based explanation should do, if completely impossible then it's no big deal I'm just going to chalk it all up to "magic".

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Fun fact: octopuses not only mimic the color of their surroundings perfectly, they can also mimic texture.

Science knows how octopus skin works. It would be possible to create cloth with elements similar to the chromatophores, iridophores, leucophores and papillae of octopus skin so as to have perfect camouflage. With a signal network similar to that behind an e-ink screen (which is widespread technology today) it would be possible to control each color and texture element individually.

We could even outdo octopuses at it. We can miniaturize electronic components so that an artificial neural network could have more neurons than an actual octopus but in a much smaller space. We can also cut the camouflage in different shapes, and we can make components with blue pigments which most octopus species lack.

Or you can just go through it like a necromancer would and wear actual octopus skin. You need to find a way to keep it alive artificially and to control its neural network. We can control the neural network of insects with current technology - maybe we could wire up some mollusks in the next decade or two.

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    $\begingroup$ Even more fun factoid: octopuses are not color blind, they just use a profoundly different mechanism to perceive color. In animals such as humans, color is perceived by superposing three images formed by three different sets of photosensitive elements which are sensitive to different wavelengths. Octopuses have only one set of photosensitive elements; they perceive color by exploiting chromatic aberration, the property of different wavelengths to focus at different distances from the lens. By rapidly varying the focus of their eyes, they are able to distinguish between different colors. $\endgroup$
    – AlexP
    Commented Dec 4, 2020 at 21:15
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    $\begingroup$ See Alexander L. Stubbs and Christopher W. Stubbs, "Spectral discrimination in color blind animals via chromatic aberration and pupil shape", in PNAS, July 19, 2016, 113 (29) 8206-8211; first published July 5, 2016; doi.org/10.1073/pnas.1524578113. $\endgroup$
    – AlexP
    Commented Dec 4, 2020 at 21:18
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    $\begingroup$ @AlexP you got a point there, I'm editing my answer. $\endgroup$ Commented Dec 4, 2020 at 21:38
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Fiber optics are thin clear fibers that take light in one end, contain and warp the light along its length, then project that light out of the opposite end. If you were to weave fiber optics through a sort of suit such that you always have ends of the fiber sticking out on opposite sides of you, the you could organize the fibers in such a way that the light hitting your backside would be projected in front of you in roughly the same colors and patterns.

That said, I would recommend a skin-tight suit rather than a flowy cloak. This is because a cloak will fold in shift causing any patterns behind you to be distorted based on how the fabric drapes on you at any given time.

If you want a true "cloak" that does this, then your cloak will need some manner of proprioception to be able to adjust how it projects light based on its current shape. The best way to do that is for your cloak to actually be alive. An octopus can do this quite well; so, your cloak may actually be some made up distant relative to the octopus that has some manner of symbiotic relationship with its wairer.

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You know how some smartphone apps can detect rotation? Image millions of tiny smartphone screens making up the surface of the cloak, sort of like how millions of pixels make up the surface of a TV screen.

They each constantly capture the background at different angle, depending on which direction each screen is facing. Now, immediately displaying what the screens sees will turn the cloak into somewhat of a mirror, and we don't want that.

That's why each tiny screen detects any rotations precisely, and only displays the captured colors when facing the right direction.

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