“Ok,
mister smarty-pants Math Guy who thinks he’s a color scientist, answer me
this! Just how many colors are there?
Huh?” I get that question all the
time. Boy have I got an answer for you. Or maybe a whole bunch bunch of
answers…
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This
blog is dedicated to Jerry Nelson, the voice of The Count from Sesame Street.
Jerry died August 23, 2012.
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The Count
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Three
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The
simplest answer is that there are three colors: red, green, and blue.
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On
the off chance that you don’t believe me (maybe you were gonna say there are
more?) pull out a magnifying glass, or a microscope, and look at your
computer monitor. Unless you happened to grab a scanning electron microscope[1], you
probably see something like the image below. Your computer screen is a
combination of red, green, and blue dots. Every color that you can see on
your screen is a combination of those three colors.
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Picture of red,
green, and blue pixels on a computer screen
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For
the sake of honesty, I have to say that this last part was something of a
lie. Not really a lie, but perhaps misleading – like telling your wife that
you are out with “the guys”. The thing is, you can’t get every possible color
on your computer monitor. You can get a whole bunch of them, but have a look
at the chromaticity diagram[2] below.
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The chromaticity diagram,
showing the gamut of a hypothetical computer monitor
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The
black triangle shows a hypothetical gamut for a computer monitor. The three
vertices of the triangle represent the colors of the red, green, and blue
pixels. By mixing the colors, you can reach any color within the triangle.
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You
will note that there are colors that are outside the gamut of this hypothetical
monitor. In fact, it is impossible to build a computer monitor with three
fixed lights that will display all possible colors. Chromaticity space is
bowed out, so you can’t make a triangle with physically realizable colors
(colors within the horseshoe shape) that covers all possible colors[3].
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Here’s
another fun experiment. Go into Photoshop or Paint or whatever program that
allows you to select colors. Try to make orange. Not only can’t you find a
word to rhyme with orange, but you can’t make a good orange on a computer
monitor[4]. The
best I could do looks a little brownish.
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The best orange I
can make on my monitor (RGB = 255, 192, 0)
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So,
my first answer to the question is that you can make good percentage of all
possible colors out of just three colors. Four colors might be a bit better.
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Seven
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How
about the number of colors in the rainbow? The colors from the rainbow can be combined to make
every possible color. Isaac Newton did some research with prisms and sunlight, and
decided there were seven colors in the rainbow: red, orange, yellow, green,
blue, indigo, and violet (ROYGBIV). The other colors I get, but what about
indigo? I’m not sure I even know what indigo is!
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Here
is my explanation of how indigo got into the rainbow. Newton saw a big section in the blue that seemed just too wide to be a single color. Now, Newton was something of a mystic, so he saw a fundamental
connection between the seven elements, the seven planets, the seven
notes of the tone scale on the piano, and the seven colors of the rainbow.
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Or
maybe he looked at the color just below 500 nanometers, and rather than call
it light blue or cyan, he decide that was blue. Having no other name, he was
forced to use indigo to name the color that I might call blue or possibly
dark blue. This is at least plausible, since the word “cyan” didn’t come into
use in the English language until 1879.
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My
second answer to the question of how many colors there are is seven, or maybe
six.
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Sixteen
million
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Now I’m going to go to the other extreme, and claim
that there are 16,777,216 colors, and that my computer monitor can prove it.
Those of you who recognize this number as 256 X 256 X 256, will immediately
understand that this is the number of RGB combinations you get when you have
256 levels of red, and 256 levels of green, and 256 levels of blue. If you do
not recognize this number I’m sorry, but you are a poor excuse for a computer
geek.
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Just because I can go into Photoshop and make 16
millions colors, does that mean there are really that many colors? The image
below might persuade you that there are (possibly) not that many. One of the
rectangles has the RGB values 255, 255, 255. The other has the RGB values
254, 254, 254. I don’t know what you see on your screen, but I can’t really
tell the difference.
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In other words, while there are 16 million possible
combinations of RGB, not all of them are distinct “colors” according to the
eye.
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Which rectangle is
brighter?
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My
third answer is that there are 16 million colors on my computer display, but
that might be a little bit of computer hype.
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Eleven
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I
taught an algebra class at UW Milwaukee. One day I gave a pop quiz to my two
classes. I asked them to take out a sheet of paper and a writing implement. I
gave them two minutes and asked them to write down all the single-word color
names that they could think of.
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The eleven colors
that everyone can think of
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I
had 50 students that took the quiz, half male and half female. Almost
everyone – 48 of the students – came up with the names of the eleven colors
in the picture above: white, black, gray, red, orange, yellow, blue, pink,
brown, and purple. If I remember correctly, there were two students who said
that their art teacher told them that black is not a color; it is the absence
of light. So that explains that. What do art teachers know?
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The
next two colors down the list were silver and gold, each with about half of
the students recalling those colors. I am going to argue with the art teacher
that silver and gold are not true colors. They are gonio-apparent effects.
And I am right, since this is my blog.
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So,
my fourth answer is that there are eleven basic colors that everyone can
recall.
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An interesting thing showed up in the
data. There was a statistically significant difference between the number of
colors that the men could recall versus the number that the women could
recall. Men averaged 15, and women averaged 18. Not a big difference, but my
sample was wide enough that it was significant. Now, it could be that my
sample was not representative of the population since there is a bit of a
gender difference in math performance and this was an introductory algebra
class taught in a college. OR it could be that women are inherently more
color conscious. I have no real explanation, other than stating what I
observed.
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The
student with the most colors was a female art student, who recalled 29 colors
in the two minutes allotted. I have given this test to a number of other
times, in particular, to my wife. In
two minutes, she was able to recall over 50 single word color names. After
the two minutes were up, she kept writing down single word color names for a
few hours after, eventually compiling a list of nearly 250. Can there be any
question about why I fell in love with this woman?
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Answer
number five: there are somewhere around 250 colors that my wife can name.
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Something
like fifteen
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I
performed another experiment, this time on myself. Unlike many of my other
experiments, this one did not involve mind-altering chemicals. It involved
colors. I started with a big bucket of possible colors, and tried to assign
each of these to a color family. I started with the eleven basic colors as my
names for color families.
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There
were a lot of colors that fit in more than one family. For example, yellowish
orange belongs in both the yellow and the orange families. And reddish green
fits into both red and green[5].
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As
I went through my bucket of colors, I came up with a few sets of colors where
I wasn’t comfortable with putting the color in any of the families. One group
could be called beige, taupe, off-white, or possibly eggshell. These were
colors that were really not white, but they were not saturated or dark enough
to be called brown or yellow. Another misfit color was tan. Is it brown, or
yellow? Not really either, I think. Or maybe it’s really brown.
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Another
group that didn’t seem to have a proper color family included the colors
coral and fuchsia. Were these red, or orange, or maybe pink? I couldn’t
decide. Maybe it is in the purple family? Nothing seemed to fit
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And
then there was plum or burgundy, kind of a brownish dark purple. Maybe sea
foam was another group, and that group might include the color that my wife
argues with me about. Cyan, turquoise, aqua, powder blue, sky blue, teal, periwinkle,
azure, cerulean… (Are you kidding?!?!??
Periwinkle doesn’t belong with those colors!)
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I
count three or four or maybe five additional color families, so my sixth
answer is that the total number of color families is around fifteen. But, I
have no idea what a different observer might say. I hesitate to run this
experiment on my wife.
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One
hundred fifty or two thousand
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It
wasn’t that long ago that the biggest box of Crayola crayons available (with 96
crayons) was proudly displayed on my desk. Today, I see that you can buy a set
of 150 crayons for the low price of $14.97. A must have for any serious
color scientist. My birthday is coming up, by the way.
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Crayola 150-Count
Telescoping Crayon Tower
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Crayola
is not the only company that is compelled to add more colors. Pantone just
recently announced the addition of 336 colors to
their color formula guides, bringing them up to “1,677 chromatically
arranged color choices to unleash their passion and let their creativity
soar.” I heard many passions unleashed by printers at the necessity to drop
another $100 on their color matching books.
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Not
to be outdone, the Valspar American Tradition paint swatch book has 1,764
colors, including “Homestead Resort Parlour Raspberry”, “Misty Morning Blue”,
and the very popular “Swampwater”. Swampwaters were very popular when I was
in college. No one knew what went into them.
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So,
the number of commercially distinguishable colors is somewhere between 150
and 2,000. My seventh answer to the question.
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Two
million
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Now
we get to some more scientific answers. Let me make the question a bit more
precise. How many distinct colors can be reliably distinguished by people
with normal color vision?
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The
quick and dirty answer comes from looking at the bounds of CIELAB space[6].
CIELAB space was designed so that
one step in any direction is approximately “just noticeable”. The value of
the lightness value goes from 0 to 100. In the red to green direction there
are let’s see, how many steps? Lemme check my copy of Wysczecki and Stiles.
Hang on a sec… Still looking…
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Ok,
so they don’t say how big color space is in that direction. Or in the blue to
yellow direction. Let’s just assume that there are something like 200 steps in
each direction. That means that the rectangle that fits all of color space is
100 X 200 X 200, or about four million.
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Of
course, this assumes that color space is a box-shape (rectangular prism). But
color space is not rectangular. Maybe it’s more like an ellipsoid? My buddy
Adam has referred to the shape as a “space potato”. Let’s just say that it’s
an ellipsoid, in which case, the volume is about half of the volume of the
box, or two million. Answer number eight.
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Some other
number?
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How
many lies have I told so far? Well, I need to admit to another one, or at
least another misleading statement. (Honest, I was out with the guys that
night.) I said that “CIELAB space was designed
so that one step in any direction is approximately just noticeable.” I did
put the word “designed” in italics to tip off that this might be a white lie.
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I
have to admit that, yes, this was the design goal, but it is not really all
that exact. For example, if you take five steps in the direction from
saturated yellow to really saturated yellow, you will just barely be able to
tell the difference in color. On the other hand, if you have a color near
gray, you can get away with only about half a step before you can see a
difference.
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This
means that the reconnoitering in that last section is a bit flawed. What’s
the real number? I honestly don’t know. I have some ideas on how to compute
it, though. I do know that there are only about 70 steps in the lightness
direction, whereas CIELAB says there are 100.
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My
ninth and final answer: Someday I will actually write some code to figger it
out, but I suspect the number of discernible colors is around 689,262. Then
again, maybe it’s the Count’s
favorite number: 34,969.
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Conclusion
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So,
how many colors are there? I dunno. It depends on how you ask the question
and who you ask. Pick a number between 3 and 16,777,216.
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[1] SEM images are still back
in the days of black and white. If you see an SEM image with any other colors
in it, it has been colorized. Someday, someone will figger out how to make
electrons with different colors, and then the images will be really, really
cool. I think I’ll go file for a patent on that idea.
[2] The chromaticity diagram
was an early attempt at trying to turn the spectral response of the eye into
something that explained our perception of color. It was replaced by other
mathematical models (in particular, CIELAB), but is still the easiest way to
understand the gamut of a set of light sources.
[3] Sharp introduced the Aquos
Quattron display in September of 2010 which added a fourth color of pixel,
yellow. For this monitor, the gamut is expanded into a quadrilateral that gives
you more yellow and orange colors.
[4] Speaking of orange… I think
that carrots are a richer orange than oranges are. I think we should swap the
names of these too foods.
[5] Ok, I was just kidding
about that one. Reddish green isn’t a color; it’s the name of the band I am
going to form after I retire from all this color stuff and learn to play the
sax.
[6] CIELAB was the next big
step forward in coming up with a measurable number that corresponds intuitively
to our perception of color. For dinner, a movie, and plane tickets, I will come
to your living room and give the CIELAB lecture to you and ten of your most
intimate friends.
we need look no further than Joseph and the amazing technicolor dreamcoat.
ReplyDeletethe answer is clearly 29 (or maybe 27, or 26 if you're an art teacher).
red and yellow and green and brown and
Scarlet and black and ochre and peach
And ruby and olive and violet and fawn
And lilac and gold and chocolate and mauve
And cream and crimson and silver and rose
And azure and lemon and russet and grey
And purple and white and pink and orange
And blue
Newton, phah...Tim Rice and Andrew Lloyd Webber have the answers (except for silver and gold.....oh yeah, and black)
Great musical, Steve! That totally slipped my mind. :)
ReplyDeleteJohn, what I forgot to say was thank you for a fantastic article
ReplyDeleteGreat article John. I thought the CIELAB point was especially interesting. If there are roughly 2 million "just noticeable" steps in CIELAB would that mean that the current standard bit depth of 8-bits/channel is sufficient for even the largest color gamuts? I've heard a lot of concern about banding with 8-bits and wide gamut but it strikes me that 16+ million colors might be enough headroom except in the most extreme, not found in nature, cases.
ReplyDeleteThanks, Jeff, for seeing a very practical consideration of this somewhat fanciful discussion.
ReplyDeleteAre 8 bits enough? It would seem that maybe they are, except that they might not be distributed appropriately. The eye is nonlinear. At the high end (near 255) we might not notice a change of even a few gray levels. At the dark end, our eye is more sensitive, and one gray level might be huge.
But, on the other hand, cameras are historically not linear beasts. They have a gamma associated with them, which boosts the midrange. Industrial cameras used to have an analog circuit to do this gamma. Today they generally have 10 bits or so feeding into a look up table to make this gamma. There is usually a switch to turn this off.
As a result, there is compression in camera images at the high end, and stretching at the low end. This means that the camera sees something more similar to what our eye sees, so 8 bits isn't so bad.
But on the third hand, images don't all come from cameras, and are often displayed on a monitor. The whole gamma thing came up back when we were using CRT displays, which are very nonlinear. We needed to boost the midrange to make images look correct. Rather than fix the monitor (maybe by adding a profile) camera manufacturers jumped on a solution.
Today, monitors are closer to linear, so... I dunno what this means! I'm confused. Is there a lookup/profile between the monitor I am looking at right now, and the image that is displayed via Windows?
I guess... if an image has a gamma associated with it and it is understood that the gamma has been applied, and what the gamma is, then 8 bits might be just enough.
You may recall prior to softproofing, drum scanner operators could only trust the screen tint Atlas books. These were printed with the printers own press, paper and inks. The step increment bewteen blocks or patches was 5%. So, from 0-100% there wer 20 steps for each color. 20C x 20M x 20Y = 8,000 colors. Adding K for another x20 (160,000) was redundant and not needed.
ReplyDeleteSteve Suffoletto SSuffoletto@BuffNews.com