The Amazing Math behind Colors! 

There is one important thing, that is easy to miss: the values 0..255 in "RGB" are *not* true RGB values - they are square roots of RGB values! That means, that the "middle" value of 128 is not 50%, but only 25% brightness. If you mix colors in that non-linear "RGB", you'll get darker colors, than they should be! The reason for that is CRT monitors, that had quadratic response to input voltage. To save money on consumer side, they decided to put correction on the production side. Also, human perception is more sensitive to darker colors, so it was also a kind of proto-compression. This is the #1 mistake of programmers, who work with colors - it has even snuck in a common software, like browsers. If you mix two RGB values, you should always square them first, mix, and then sqare root them. * To be exact, they are not even square roots, they are 2.2-degree roots.

I am approaching the age of seventy. I have found myself confused over the course of my conscious life by every account of colour that I have ever come across. This is the very first account of colour which I have found comprehensible. It is the best thing on the subject I have ever seen. I learned an immense amount from this video, the conistent quality of which astonishes me. I salute you, Kuvina Saydaki. Thank you, thank you, thank you!

This is probably the best explanation of color on the internet. And believe me I've watched/read so many. But none of them answered all the questions I had about color vision and color spaces as clearly and as detailed as this one. Brilliant. Looking forward to watching the rest of your stuff!

this is so well made :D

ive been reading stupid scientific papers about CIELAB and all these color spaces for months but this is the first time ive genuinely felt like i had an intuitive understanding on this topic. Thank you.

I'm so happy this got recommended to me. This video is criminally underrated!! The quality is insane. Thank you for making this. It was a very interesting watch. You have a very good sense for explaining things :D

I've heard claims floating around that you can see invisible Colors by abusing the fact that when neurons fire too often their outputs are ignored by the brain. The idea is, for example for hyper green you can stare at a red image for a long time until the neurons that carry short cone information are deactivated and then quickly switch to a green image while those neurons are still deactivated and that will let you see hyper green but I don't know how true it is

For years I gave a project to my Linear Algebra classes to research and describe how vectors and linear transformations have to do with supposed "color spaces". Congratulations! You've beaten them all 😂. This is officially one of my favorite videos on RU-vid.

The very moment I was thinking "Is he going to leave _anything_ out?" you broke out an explanation of converting hex to decimal. It just doesn't get any better than this.

This is single handedly the best, most robust, comprehensive and informative video about colors in all of the internet! I hate that the algorithm took 10 freaking months to bring this to my feed! I was geeking out throughout the whole thing. The marriage of the topics of arts (color), physics (waves), biology (perception), chemistry (pigments), astronomy (stars), computer science (hex & HSV) and math has never been this seamless and well connected in any video I've encountered. It clearly shows how much you yourself have been intrigued in these topics and how much you've thought about the relationships between it all, and as someone with shared interests, I literally turned into the neuron activation and pointing rick dalton memes every other minute. Not only that, but every time you went onto a small tangent, you made sure to sprinkle in a "well, no, actually" and proceeded to make the viewers informed about the intricacies of the tangent instead of simplifying it too much and moving on. (For example, fact about responsivity and normalized was new to me. And also Newton taking a dumb liberty + supernumerary bands forming purple. And also how Sun's spectrum isn't ideal due to non-uniformly traveling light.) Absolutely outstanding job! If I were to provide some suggestions, the first would be at about 11:45 where you start introducing colors (purple) outside the curve. You could've sprinkled in stuff like how the light waves, the conversion of light to signals, and the interpretation of signals to color are independent phenomena. Meaning, the brain doesn't care whether it is sensing 'light', but only that it's receiving some kind of 'signal' about the environment. Consequently, if the brain is receiving a signal that peaks at the short and long cones, it will find a way to interpret that as well. But how would the eye even manage to sense receive light that simultaneously triggers both cones if all the wavelengths in the visible spectrum only trigger colors in the curve? And the answer to that would your explanation for monochromatic and polychromatic light. I think it would be a great transitional segment to your excellent presentation. There's nothing wrong with your explanation. It's just that as someone who has studied this topic, I can fill in the gaps with my own knowledge, but a beginner might not. I think it would be cool to let viewers know that not only are colors non-existent/imaginative in nature, but also that the color purple quite literally doesn't even exist! Like, it's not even an interpretation of wavelengths by the brain but something the brain just made up! *cue exploding brain* The second suggestion would be at 30:10 where you brush over the luminance part. I am personally not well-informed about the details in this specific part, so I just accepted it as is. A bit more could've been nice. And also about how light polarization is utilized in LEDs. Anyways, this comment is long enough and you probably won't even see it. I just wanted to express my appreciation for the work and informative quality you've put into this video. You've made my day!

This is so amazing, I'm not even halfway through but this is exactly what I need. I've been learning a lot how to think about colors not only in RGB/HEX values for websites but for print over the last year, but I knew I was missing some solid fundamentals. I'm at the CIE 1931 xy Cromaticity Diagram right now, I think once I reach the end of the video I'll be totally enlightened :D

A really excellent video. As a painter I would like to add a bit about subtractive mixing. C, M, and Y are a good compromise set of primary subtractive colours but don't really make the definitive three primaries in the same way that additive primaries do. One reason is that when they're mixed, there's a loss of saturation, so while you can make a version of every hue with CMY, you can't mix every colour at full saturation. For this reason painters will often choose different primaries in their palette. With orangy red and a yellow you can make a more saturated range of oranges, but won't be able to make a strong purple with the red. With magenta, yellow, and an ultramarine blue you can make a better range of strong purples than CMY but only a duller orange or turquoise. The second issue with subtractive mixing is that you get the wavelengths that the two primaries share in common. If you had a hypothetical red pigment that reflected a pure red wavelength only, and an equivalent blue, they would mix to black! But you could have a red and a blue that look exactly the same to the eye, but that reflect more of a mix of wavelenths. These would mix to a purple of some sort. The conclusion is you can't predict exactly how subtractive pigments will mix just by their visual appearance! Thanks and best wishes, Tom

This is an excellent introduction to color math! I would love to see a part 2 to this as well, covering things like Color Rendering Index (CRI), perceptual color spaces (CIELAB, HSLuv, etc), and the different types of colorblindness. Colorblindness especially is something that's often misunderstood as a complete lack of color-processing ability, where in the most common forms just have a slight shift in the response curves for M cones (as in deuteranomaly) or L cones (as in protanomaly) so they overlap way more -- effectively, making the red-to-green side of the chromaticity chart "shorter".

Wow, this video really unified my understanding of color! Not just on screens, but in general. The explanations of the relationships between the ways we represent and model color were succinct and clear. I came in with a decent grasp of most of these concepts, but this really drove home the connections between them all, thank you!!

This is an unbelievably high quality video. Thanks.

im supposed to study wtf am i doing here

Excellent analysis of chromaticity and RGB color theory, which explains the physiological response of the eye to visible light. For your next project, I'd suggest an exploration of Opponent Color Theory, which explains the brain's psychological response to color and the phenomenon of metamericism. Briefly, the optic nerves between the eye and brain combine the RGB components from the cone cells into sum and difference vectors which the brain interprets as a pair of orthogonal color axes: a red-green axis and a yellow-blue axis. Each distinct area of color in the visual field is mapped into a position on each axis according to its chromaticity relative to its perceived background. These two-axis coordinates are interpreted by the brain as the metamerical hue of each perceived area of the visual field. Opponent color theory explains how different RGB combinations can produce the perception of the same psychological hue. Also why we can perceive shades such as greenish-blue and reddish-purple, but not yellowish-blue or greenish-red.

This is so good. You don’t know how many times I’ve tried to fully understand a chromaticity diagram. Well done!

Literally everything you could ever want to know about colours. Now I wanna build flashlights with specific wavelengths and combine them to see the forbidden colours

This is awesome I'm a scientist/ engineer and also an oil painter. I'm fascinated by the intersection of the two. Having an understanding of color science has made painting much more intuitive, while having an artistic eye for color has made life so much more interesting, since every play of light and color in daily life, is so much more apparent.

This is hands down the best video i have ever seen about color. Anything from perception, reproduction and modeling.

This video blew my mind!! Everything there is to say, everything there is to explain in ONE VIDEO! Spittin' out facts and entire collections of knowledge like a waterfall, just as you go. Incredible.

One of the most thoughtful and comprehensive videos on RU-vid about color. Amazing!

The pace, scope, sequence of presentation are perfect in this video. Would that all instructional videos were like this! You would be that person who could adequately and succinctly explain quantum mechanics in a video.

I love these kinds of in depth videos. Litterally everything you know about colors is in this video. You have answer all my questions I had about color, introduced new questions, then solved those as well. Great Job!

You’ve answered so many of the questions I’ve collected over decades of work with color in information technology! I finally understand how a spectral range from red to violet is perceived/represented in a color wheel. You’ve even answered questions I hadn’t considered. Thank you!

Congrats on being one of the SoME2 honorable mentions! This video was fantastic as are the rest of your videos, I hope you make many more in the future

I love the math behind colors. I'm colorblind (defective S-cones), so in a way it's my only way of working with all the colors. I've been working on some image recoloring shaders, including ones that treat each color value as a probability of the pixel still having that color.

Came here after watching the Technology Connections video on Brown. You did an amazing job especially explaining how the different eye cells react to wavelengths to produce our perception of color, I understand that much better now. Thanks for the amazing work!🎉❤

Thank you, all my 60-years I've seen examples of all of this but always as singular concepts, or parts of a whole, never combined in any rational way that I could grasp. Still my grasping has left some that squeezed out, the stuff that would allow me to prove to anyone I got this mostly, but I got enough for me. Thanks to this video I'll never again look at my color picker with contempt.

One of the best math videos I've seen in my life. I'm gonna suggest it to my professor of the neurosensory class

this video validates so many of my thoughts, and complaints. i absolutely agree with you about ROYGBIV and i didnt know the history. i always wondered why they ignore cyan.

astonishingly & beautifully explained: methodical, complete, the points explained in a good order, with distinction between what's actually happening vs what's perceived. ahh and the explanations are so clear and presented well graphicallyyyy! and there's the underlying light-hearted vibe tops it off. honestly, one of the best presentations i've ever seen on anything.

This is the best explanation of color space, especially how there are areas with a corresponding LMS activation values but impossible to see, always wondered about those.

Great video! I'll add one thing I discovered while looking into colors: painters refer to a color mixed with white a "tint" (e.g. ice, mint, ivory, etc. in the diagram), with gray a "tone", and with black a "shade" (e.g. navy, burgundy, pine, etc. in the diagram). They can be useful when designing a color scheme.

I absolutely love the breadth of information here. I would struggle to name a color-related topic that wasn't mentioned, and they were tied together so brilliantly!

Love what you do! Kuvina, you're genius, I am officially your fan!❤ apart from the comprehensiveness of the presentation, I am just blown away by the graphics and the sound, the overall aesthetic and idea, simply amazing!🤯 Chapeau!

This is a fantastically detailed and accurate treatment of the physics, biology, and psychology of color perception. I've never seen anyone bring it all together like this. What a great production!

I looked for a video on this exact topic about a month ago and was super bummed to not be able to find stuff aimed at beginners to these concepts like me. I resolved to just not understand any of this until youtube did its job for once and recommended this fantastic video to me. Many thanks!!

Congrats on Honorable mention! This is a really cool video -- I always wondered if colors are actually a real physical phenomena or simply a figment of the human subjective experience.

A week back I wrote a program in Java that takes any color in RGB, HEX, DEC, HSB/HSV, HSL and CMYK and converts them into all the other representations in the respective color spaces. It can also display the standard color chooser to get an input as well. While searching for ways to do those transformations I also found the conical 3d-representation of HSV. I didn't quite understand it back then and just took the formulae for granted, which worked fine and the program did what I wanted, but it was not until I found this video until I felt like I actually understand what's going on. Thank you a lot for the video! I really liked how you were able to combine so much biology, quantum mechanics, mathematics and color theory in one concise lecture. I'm pretty sure there is a lot more but this already felt like a lot to take in at once and I'm certain that I now understand this topic a lot better. You definitely got a well deserved follow and recommendation to my friends for this one!

This is the video about color I've ALWAYS wanted!!! Such a beatiful explanation of it all 😍 Omg you even named the 12 main colors around the hue circle, and now i finally have good a word to call each of them!

This is the one that made it click for me for color spaces. I'm a developer and learning color grading for videography too, and this is of immense help 🙏

Love it - Beautiful review of color language with updates through computer age. *Thank you!* This made me reflect on and better understand my 50 year journey from photography, NTSC waveform/vectorscope, optics, computers to _now_ discover the human eye/brain color "timing" concept here, and Fourier Transforms/Physics to create Attosecond Laser pulses _Oct 2023._ What a trip!

"Green?" "Hypergreen." No single video I'd seen before explains SO much about the nature of color. What a treasury of knowledge, this is. Thank you.

There is no better way to explain this! You have no idea how thankful I am! Thank you!

Great video. Really. My wife was laughing about how many times I said "Ohhh!" in moments of realization. This video made the lightbulb over my head light up a number of times, as it were. Thanks!

This is a very nice video. I teach data science at a university. when I talk about graphics, the choice of colors is always very important. I always recommend the HCL color space, which makes it easy to make "evenly spaced" colors and palletes for people with a color blindness (which affects something like 8% of all males).

This was a really good explanation. You deserve way more views on this video. I studied Physics but have recently started trying to learn to paint, and I think for this reason the RU-vid algorithm recommended me your video. And it was actually exactly what I wanted, without even knowing I was looking for it. An easy to understand but mathematically vigorous explanation of colour. I actually can't believe this video was suggested to me, it has been so useful!

Me: I wonder what aspect of colour this video will focus on? This video: YES!

This was a great submission...so much ground to cover on a subject of great complexity and some subjectivity. I much appreciate how it was concluded with the cone representation: neat amd tidy.

This was obviously a ton of work. Thank you so much. Literally every bit of information you provided was interesting, which is remarkable for a video of this length.

This video is greatly helpful for me and my students in the course "Chemistry and Physics of Colors" at Soka University of America. Thank you very much!

I love #SoME2. So many new chanels that bring such high quality content! I've always really wanted to know about how colours actually work and this video was such a good explainer! Thanks

I have been obsessing over colours for the past month and I must say, this is the best video on the matter, possibly the best internet resources short of actual books and even then it's good cuz of the video visualisations! Thank you so much

Excellent excellent video, simplified but without unnecessary reduction that obscures the bigger picture.

Best comprehensive explanation of the subject and it's not even close. Thanks so much for the video!

I've been slowly teaching myself this stuff for fun, and goodness gracious, this is like the ENTIRE rabbit hole condensed into a single video. I personally got stuck on black body stuff lol

Can't thank you enought!!! You have a tremendous talent for exploring a set of related concepts and then explaining them in a well-designed and cleanly structured manner!

I've similarly been obsessed with colors through my life (including making a color system similar to yours!) but this is the best explanation for how colors work I've ever seen!

I wanted to understand how the familiar CIE color space diagram is derived, but after reading/watching other explanations on the Internet, I still couldn't grasp how it follows from the 3D "physiological" space where L, M, S responses are separate dimensions. Your explanation filled in most of the blanks for me - now I understand it's a projection onto an equal-luminance plane. In general, I think this is a stellar explanation of color - precisely in the right order, starting from physiology, and no glossing over important details. It must have taken a lot of time to structure this so well. Terrific job!

What a detailed and comprehensive explanation! I thought I knew the subject, but it turned out it was only a small fraction

Great work on this video. I've studied color stuff for years (wrote RAW converters for cameras, image processing pipelines, etc..) and I still learned things! Keep up the good work!

This video is astonishing. In addition to being a bona fide colour expert (a journeyman pre-press technician since the 1990s), I have a solid background in physics and quantum mechanics. And yet, I don't think there was s single minute in this video in which I did not learn something new, or clear up a misconception that I have carried for a long time. Bravo!

The highest information density I have ever seen in any video

Corrections/Clarifications 1. 37:10 I misspoke and said m1 instead of m2. What is shown on screen is correct. 2. 22:12 On screen it says λ = f/c, but this is wrong. The correct formula is λ = c/f. 3. A common question: Why does a spectral violet (~410 nm) appear slightly reddish, when it's only the short cones that are active? Shouldn't it appear the same as a pure spectral blue (~440 nm)? I have been told by several commenters that the responsivity function for the long cones has a very small secondary peak around the shorter wavelengths like violet. However, I have found conflicting information on this. Either way though, the way that the brain makes colors is very complicated, involving something called the opponent process. en.wikipedia.org/wiki/Opponent_process The reason this makes spectral violet appear slightly reddish can be found here: en.wikipedia.org/wiki/Violet_(color)#Optics 4. It is possible for some people to see impossible colors by staring at a single color in order to "tire out" one of the cone types. Then, when you look at a different color, some of the cones don't activate like they usually do, because they're "worn out" so to speak. The effect only lasts a few seconds. But be warned, you should never try this with bright lights. They can do permanent damage. More information can be found here: en.wikipedia.org/wiki/Impossible_color 5. In the video, I never explicitly mentioned it, but the Arabs discovered all that stuff about optics way before Newton did. Notably Alhazan en.wikipedia.org/wiki/Ibn_al-Haytham#Book_of_Optics

Holy shit this is such a comprehensive and efficient video i rarely get the pleasure of witnessing such a perfectly paced masterpiece such as this

I love the scent of complicated Math concepts in the morning😌 I've been trying to wrap my mind around connecting colors and Math but until just now, i had no RU-vid video to teach it to me. You just made my day! Please respectfully go into as much detail as you want about color+Math.

This is the video I was looking for! Thanks, Kuvina, this is incredible!

I had no idea this was gonna be so interesting!! Really great video covering so many different topics in that intersection between your passions of math and color!

this is by far my new favorite math channel 11/10 videos

Holy Fuck, so much information in a single video. This is without a doubt a classic in RU-vid educational videos

This is the he best video I have ever seen explaining color in all its human manifestations. Thank you for taking the time to put it together.

This video is by far the best I’ve seen on Color science. Great job. Thanks for the hard work. Cheers

Kuvina, this is, and I can't stress this enough, BY FAR the most comprehensive explanation on colors. It answered basically all my questions. Thank you a lot. I will share this video to everybody, now!

A lot of information -> great editing -> simple and straight explanation -> good job! This is a great video about color and the mathematics!

This is, hands down, the best yt vid about the science behind colors

I didn't see how long this video was when I clicked it and only now, 23 minutes in, I realised I've been watching for that long, wow. I've been switching from video to video this evening and somehow this got me stuck. Good choices of what to what keep and cut. Amazing video 👏

When I saw 1880 views, I had to double check because it looks like a 1.8M views.

I love how it starts with the details of how light is percieved before introducing how colour systems work

Brilliant and very learning walkthrough of something I thought I knew. I stand corrected - even after close to 40 years in tech (broadcaster). Thanks a lot!

So comprehensive and has so many insightful explanations of cool colour visualisations!!! i love seeing these different ways to express colour.

Great video! Covers pretty almost all of what one might want to know about average human color perception and ways to represent those colors. My main concern is with the "average" part of that description. While it's still one of the better resources, there are much more resources on the common cases than the less common ones. One display manufacturer tried to advertise a display with a fourth color channel, which increased its gammut by... _absolutely nothing_ because it didn't actually include any way to emit a fourth wavelength of light. Aside from that, other comments have mentioned phenomena like impossible colors, which are points in the LMS cube that are actually unreachable not only by any single wavelength, but also any combination of wavelengths. Several of these can still be percieved in spite of this thanks to the eye's adaptability resulting in the responsibility to specific colors changing. The real fun comes from individual people with significantly different responsivities from the norm. These include colorblind people such as dichromats and monochromats. These people only have 2 or even just 1 color receptor, in addition to the rods, which are only sensitive to brightness. Naturally, having a different number of cones, or having cones with significantly different responsivities would result in completely different color gammuts and chromaticity diagrams. That said, it can be very hard to find examples of these. Even rarer are the _tetrachromats,_ which possess the 3 usual cones, as well as one of the mutant cones that are normally found in colorblind people. Naturally, I don't think I've ever an LMM*S color _tesseract_ before, nor a 3D chromaticity diagram, even ignoring the challenges in actually rendering these shapes with or without the extra colors. This may be related to the people who actually have these conditions being rare enough (or well hidden enough) to not give enough data to make accurate measurements.

Thank you for the video. I learned things. I was hoping you would mention chimerical colors, aphakia, or tetrachromacy. Relearning things in more depth was nice, too.

What a great video! I had a very superficial idea of how colour space works but this has clarified things enormously and tied what I already knew together. Thank you!

thanks, this is probably the best and most thorough explanation of color in one video i've seen! i will rewatch this again and again. thank you!

This is by far the most comprehensive and easy to digest explanation of color I've seen. Great work!

what an amazing video !! i'll be recommending this a lot. i've been reading a lot about TV tech, lights and color lately and this not only has summed up lots of it, but it also cleared up some stuff i had missed.

Congratulations on such a comprehensive overview of a wide topic. Very well done. Thank you.

Exhautive description that seems to cover dimensions that traditiinally are kept separate like the role of our brains (and attendant unique sensory expereince) in the apercception of color. And yet- the math driven by a desire for systemization is compelling. Your final arrangements are a breath of fresh air because they are oriented in a circular base other than 6 and provide a home for white and black. thank you for your curiosity and drive to make sense (literally) of this subject.

You have combined so much information from all the fields into a single video here. Thanks for producing this.

This is the most complete and easy to understand video about colors I've seen

This answers so many questions I’ve had, and answers them so well and understandably. Thank you!

I have been eagerly trying to understand precisely these concepts for months!!! Here lies all of it, packed in just a 40 min video. Thank You. ✨✨👏👏

Wow, very impressive how you tied it all together, yet still made it understandable!

This video is just so impressive. I knew a bit about RGB vs CMYK vs HSV, light sources such as white LEDs (often blue with yellow phosphor), etc, but this one video added so much more. Thank you for making it and for the time and effort that went into it. I only wish I had seen something like this about 15 years ago.

Totally fascinating. Answers a lot of questions that have been piling up in my mind for about 20 to 40 years. Mind blown. This is what I'd have expected when studying physics in 1985..

As a colour blind engineer, I found this excellent explanation fascinating because the math helps me understand something that never made sense to me. This leads me to a question about fashion…Are frequencies of colour similar to sound in that some sounds are not appealing, like if I tried to select several keys on the piano to form a chord. If a musician played the piano, they know what keys form chords and those chords may make you feel different emotions, ie major chords vs minor chords. Are colours similar? My wife will often tell me the colours I have chosen for my shirt don’t “work” with the rest of my clothes. Have I just chosen materials that reflect light that for mathematical reasons are noise, like random keys played together on the piano? Or are colours that go together just a current fashion trend where right now they are acceptable, but in a few years of months they would not be worn together?

Very well done, thanks a lot. I really appreciate the depth and how one subject led to another, good structure and good coverage of all the questions I came up with as I as watched :)

Honestly one of my favorite videos ever. Amazing job!