Monday, January 5, 2009

Color Wheels and Color Space

Colors wheels and systems are really interesting to me. There are so many fascinating assumptions made with them, and systems based on them, all in an attempt to understand how color can be organized and defined. One would think this would be simple, but it isn't necessarily. To start with, the so called color "wheel" is a total fabrication, primarily by Issac Newton, who decided to tie together the two tails of the spectrum- the infra-red and the ultra-violet, as they were "similar". But this has no basis in nature, its just an organizational tool based on a coincidence. In addition, at some point, he decided that the spectrum was composed of 7 colors only. As there were 7 planets at the time, and 7 notes in the Western music scales,this made a tight little bundle, but one wonders if which came first, the idea that there was yet another buried magical 7, or the reality. Munsell, in his system, names 10 colors, and it seems likely that its all about fitting round objects into square holes, and not that there is some underlying magical number of colors.

Consider,if you will, and as I have been, the puzzle of not how many colors there are in the world- but of how many colors can be painted. This seems like a puzzle that could be solved, or at least closely estimated. One could just take paint, and start painting. I've spent some time with this trying to model it on the computer, and although we have been told that the eye can discern millions of colors, I am fairly convinced this is an gross exaggeration that doesn't pan out. I think it is probably less that 100,000 or so, if that, and that we can paint far less.

Start with just two pigments. Say a white and a ultramarine blue. The blue is very dark, and of high chroma, so we'd expect a lot of possible mixes as we proceed from one to white. As we add white to the blue, it both reduces its chroma, and its value. (I would guess that there are undiscernable changes in its hue as well, though I don't really know.)

How many steps are there that are discernable, by a good eye, in good light? Certainly we could paint more than ten. But I think we'd be very hard pressed to paint 100. This is testable, I haven't done it yet, but it seems like I could paint a long stip, say a few feet long, with as much of an even gradation as possible, and then chop it up into same size chips, and see which ones can be told apart from the others. I don't suppose that this is even an arithmetic progression in chroma of value change, though I don't know, and I don't know how to measure it. But if I had to guess, I bet there would be 50 chips on the table that you could tell were different.

With three colors a "color space" starts to happen, with more complexity, and unsureties. I do not think that it can be done theoretically- I've scratched my head on this,and the basic question is the same, with three colors, perhaps widely spaced in the Munsell solid, how many colors can be painted? If we were to paint these three colors, one to each corner of a triangle, and the require that each discerbable color get a 1x1 square, could we fit all the colors within the triangle? At first I assumed one could, but I am starting to think that something else is going on as the mix starts nearing any apex.

For example, say we take a blue and a yellow, and mix all the possible combinations of these. Say we have 50 1x1 squares of color defining one leg of the triangle, and that we do the same with blue to white, and yellow to white. And for discussion sake, say each of these legs is 50 squares long. This would make a triangle that could fit 50x50/2= 1250 squares. Which one would expect is close to the maximum number of colors that could be mixed. Perhaps it is.

However, is we now we take each of the 50 blue to yellow mixes, and in turn, we mix each of these with progressive steps of white. Do these produce 50 c0lors as well? Each in turn? Or do they repeat themselves?

I don't think that they do repeat themselves, and rather than forming a triangle, they just form a big matrix, perhaps not even square- depending maybe on the vagaries of our vision.

If we take blue and white, we get (say) 50 colors, with the color just before white with just a hint of blue, and very low chroma and value, as we'd expect. But let's say we started with blue with just enough yellow to make a green, then again, we could expect roughly 5o steps, perhaps fewer in this case as the yellow is of high value, but the question is, just before it gets to white, can we discern it from the adjacent mixes, do they start to meld together? I suppose it depends much on the eye- but that there is more discernability than one would expect, and therefore, more colors that a 'color wheel" or a color solid, actually suggest.

More on this later.

No comments: