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February 24, 2013


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A series of occasional articles on the intersection of art, math, and computers.  See the first article, "Primary Colors", here:

Magenta isn't a thing...

Isaac Newton wasn't the first person who noticed that when light passed through a prism, it transformed into a rainbow of colors, but he was the first to figure out (roughly) why. Before him, people had supposed that the prism somehow corrupted the color of the light. Newton took that rainbow, passed it through another prism, and "re-assembled" it into its original state (white light), and deduced correctly that white light is actually made up of many different colors. He even charted it out, making a linear bar of all the colors, from red on the left to violet on the right.

But then he noticed that a popular visible color -- magenta -- was not in the spectrum.  Magenta was really a combination of red and violet. So Newton took the his linear color spectrum and made it a circle, joining the red and violet ends, thus giving birth to the color wheel that is, in some form, part of every beginning art class today.  This was work he did between 1666 and 1672; he was in his 20's, and well on his way to laying the foundations of modern physics. You should be awed.

...and neither is Roy G Biv.

Newton's spectrum of visible colors is a continuous gradient from red to violet, with no clear delineation between the colors. How then did we end up with red, orange, yellow, green, blue, indigo, and violet, the seven colors that we all memorized as Roy G Biv? Well, seven was an important number back then: 7 days in a week, 7 known planets, 7 musical notes in the diatonic scale. The idea of that sort of unity was important to the thinkers of the day, even if it made for a somewhat arbitrary division, and led to a color wheel with uneven segments.

In modern times, when teaching our children, we tend to indulge the great man and accept his assertion that indigo is a separate color.  But in practice, the most basic color wheels quietly lose indigo, shove blue and violet together, and present a pleasing circle, symmetrically divided into six segments. We should not let this diminish our estimation of the man's genius; the basic concept is still intact, 350 years later. The middle of his circle is the white that results from combining all the colors, and the colors get more intense (the saturation increases) as we move towards the perimeter.

The wheel keeps on turning

The color wheel has continued to evolve to reflect new developments in color theory, assuming new and more complex configurations. But at its heart, it is a tool to help artists combine color in the most effective way. Three common concepts are analogous, complementary, and triadic color combinations, and these are all based on the colors' relative positions on the wheel. Analogous colors are next to each other, and they go together in a very natural way. Complementary colors are in opposite positions on the wheel, and tend to accentuate each other. A triadic color scheme uses three colors that are evenly spaced along the wheel, and these provide a high-contrast, vibrant palette.

And now for the math...

Software can represent colors with numbers, so the next logical question is: can we use math to calculate color combinations?  Of course! Using the familiar RGB notation, a color can be identified by three numbers, each between 0 and 255. To calculate the RGB coordinates of a color on the opposite side of the wheel (its complement), we do the following:

Here's our color: R(220), G(50), B(120)

We take the highest and lowest RGB numbers and add them together, so 220 + 50 = 270.

Then we subtract each RGB number from this sum:
270 - 220 = 50 (this is the new "R" number)
270 - 50 = 220 (this is the new "G" number)
270 - 120 = 150 (this is the new "B" number)

So our new complementary color is: R(50), G(220), B(150)

Calculating a triadic combination is even easier.  We just "rotate" the RGB numbers.  Starting with our original color, our triadic scheme would be:

R(220), G(50), B(120)
R(50), G(120), B(220)
R(120), G(220), B(50)

Cool, huh?  (You're a geek if you say "yes")

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OxxyJoe Featured By Owner Mar 7, 2013
Very cool as well as very (verily?) educational. Now I must wonder "why magenta is infinitely more magenta than shown"
Thesis-D Featured By Owner Feb 24, 2013  Hobbyist General Artist
The steam isn't coming out of my ears just yet, but it will eventually if you keep making these! HAHA!

Its interesting information. It could go a long way in describing why some people can perceive color better than others, and why, as we're developing, our ability to differentiate color increases. The three color wheels, to me, seem like 3 different ways artists are wired to see color until they train themselves to recognize all three, and the math behind it may be a way of explaining it.

Our eyes are amazing tools. :)
outsidelogic Featured By Owner Feb 24, 2013  Hobbyist Traditional Artist
If you think it's challenging reading it, you should try writing it! There is SO MUCH misinformation out there on the internet. To find something like when Newton invented the color wheel requires sifting through dozens of sites, and trying to distill the actual facts from all the nonsense. It makes me wonder about how new generations will conduct research. I mean, it would have been faster for me to get a decent biography of Newton out of the library. At least that information has been curated, or vetted, and is not just a collection of blatantly wrong stuff packaged as facts.

I must say that wikipedia seems to be the most consistently credible source out there.
Thesis-D Featured By Owner Feb 24, 2013  Hobbyist General Artist
Yeah, information centers are often bloated and hard to get what you're looking for. You'd think the technology would make things easier! You see those old posters for ideas for what the future would be like, and this was back in the 40s and so, and they were really, really reaching it seems, because none of the stuff they thought we'd have by now is a reality...or if it is a reality, its well hidden from the public.

Where are our personal family rockets, robot maids, and hover cars? It's amazing how we can think all this stuff up and create shows and movies like Star Trek and Star Wars, and not come anywhere close to creating the real thing yet! Anyways...

Its funny you mention wikipedia, because I remember a professor in college telling me we couldn't quote or reference that site and she would not accept our work if we did. Apparently, its too easy to edit the information there and screw it up.
outsidelogic Featured By Owner Feb 25, 2013  Hobbyist Traditional Artist
Wikipedia is still a source of controversy in schools. Both my kids have teachers who won't allow them to use it for research projects. I think that's wrong, because it's part of everyday life now, and people need to learn how to consume that kind of information...cross-check it and verify it with several sources.

Yeah, where the heck are our flying cars?
Thesis-D Featured By Owner Feb 25, 2013  Hobbyist General Artist
Well, I think some professors may have a chip on their shoulders or swollen egos or pride and relish in having something done their way. Of course, theirs isn't the only profession where people have that "I paid my dues now its my turn!" attitude. I do find it slightly rude when a professor, especially a female professor insists on being called Professor also. It just smacks of pretentiousness sometimes..and the general stupidity or ignorance of the student body in a classroom setting is unsettling. You think that when you're in college you're really learning, but its not always the case, you're just busying yourself until you get them credits. It seems more like a transaction than a learning experience. Of course, this completely turns around when you get a good Professor and a mature set of peers. But that's another discussion!

Yes, where are our flying cars! But where are our replicators?! I don't know much about Star Trek technology, but those replicators that can make any food you want instantly are pretty cool....though it would do millions, if not billions of people out of a job! :XD:
outsidelogic Featured By Owner Feb 26, 2013  Hobbyist Traditional Artist
Well, you just burned a wide path right through post-secondary education: teachers, students, and college itself. Take no prisoners! But yeah, I hear you; education can be frustrating sometimes. It never bothered me too much because I was never a very motivated student. But my oldest daughter, who thankfully is not taking after me, wonders what she is doing in class sometimes.

But I have to ask: "...especially a female professor..." ?
Thesis-D Featured By Owner Feb 27, 2013  Hobbyist General Artist
I'm also not saying college or an education isn't worth it or that anyone who has put money, serious or otherwise, into it is a fool and that their degree is worthless. I apologize if it came off that way and if I've offended you or any one that reads or has read this.

This subject is a grey area for me, and as such, I don't see it strictly or always in a positive or negative light. Its sort of both and neither at the same time.
Thesis-D Featured By Owner Feb 27, 2013  Hobbyist General Artist
Oh, and I'm not referring to myself in my last response, just in case you're wondering. Not about the drunken frat boy sex addict or the degree that's worth salt now. :XD:
Thesis-D Featured By Owner Feb 26, 2013  Hobbyist General Artist
I think that college is often exaggerated as a place of "higher" learning when sometimes its just a big boys version of high school, or high school all over again, only difference being you have more freedom, the teachers have more authority, and you're paying. When I look at the plan for how some professors plan to teach their students, it really does seem lackluster or infantile. I dropped a class once where the teacher was having us do printout worksheets as the bulk of the teaching. Ah.... no. Sorry, not happening. I'm not paying money, even if it is financial aid money, on worksheets and print outs. Teach me yourself, get up their and lecture, and pass your wisdom on to me, and then you deserve your title. Otherwise, its just useless regurgitation, and it doesn't take a professor to do that, an elementary school teacher can do that, not to denigrate elementary school teachers.

I'm jaded with good reason. I think the system is just set up to milk us so you get a piece of paper in the end that says you're qualified to do this or that. All it proves for certain is that you can regurgitate information. It doesn't say you have any experience, its just like some masonic ring or something that when you wave it it lets other masons know you're in the club. LOL, but it doesn't mean you're qualified, it just means you paid your dues and "THOU SHALT PASS!!!" Excepting your major and area of focus, is any of the information you learn in college necessary for your future well being? I'd argue its not, not any more than what you learned in high school will amount to a life or death situation or ability to get into and earn further gainful employment. Its just a rehash of high school, but this time they're charging you for it. College doesn't necessarily produce better, smarter people, either. It just means people made it through and paid general enough attention for short periods of time to pass exams. A drunken party frat boy who has more sex than studies can do that. He just has to regurgitate long enough and then let it out and never pay it a second thought again when its over. The piece of paper he gets at the end says he's worthy. Is he really? He might be worse off for having had the typical "college experience" than he was before he even went to college. In fact, it might have been the college that screwed him up! LOL!

Your daughter is right to question her education, and you, as her father, have a responsibility to make sure that by hook or crook she's getting a good one. You seem like an intelligent, moral, family man and I'm sure you're doing just that. We, as a society are just "passing" people through the system, I feel, but we call this "graduating" them. Graduating them from what and to what? BAs and even Masters degrees in some cases, aren't getting people into jobs like they thought it would anymore. You hear about it all the time now. These people end up working retail or even fast food because the nice paying job they thought was waiting for them, as if the degree is some sort of reservation, fell out from underneath them. Nothing is guaranteed in life, especially not with things the way they are now in this country. Now, we're just grateful to have a job to go to, and rightfully so. We should have been grateful from the start.

My name is Damien Jones, and I approve this message (rant)!

(PS: Well, in my case in particular, there was one professor who insisted on professor when someone called her "ma'am", I believe. Also, I think it might have even been in the class overview sheet given out at the beginning of the semester. Literally, that she prefers "Professor", and not Miss or Ma'am. My point is, I think women tend to be more sensitive about this than men for any number of reasons. I haven't met a single male professor who didn't appreciate or accept a good "sir". I could be wrong, but it seems like its more of a concern the women have than the men, and I doubt its not because of sex or gender, but precisely because of it. I understand that the title is an achievement, and is sex and gender neutral, but could some feminist/sexist element possibly be a part of what causes it also? Hmm, I don't know. A woman in this position shouldn't take offense at a polite "ma'am". As long as you interchange "professor" with "ma'am", etc, it should be fine, no? It seems reasonable to me.)
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