Overheads

ok this puzzles me a bit.

You know the overheads old professors that don't know how to use powerpoint (or refuse to, whatever) uses. What would happen if you make, like, a gigantig overhead. And put a continious strip of color on a transparancy (ignore the fact that we're talking about color PIGMENTS here, so that my "theory" would hold anyway) but is color continious? Like, would you start to see "pixels" on the overhead if you had one sufficiently large? Is color countable, is it discrete or is it continious? With color, i'm more than likely refering to photons with different wavelengths.

True light can be represented by some function f(x) where x=frequency and f(x)=quantitiy of photons with frequency x.  Humans interpret f(x) in a manner that reduces it to just three variables, RGB (or hue saturation luminescence if you prefer).  This is why your monitor can display colors that look just like real life by manipulating just three families of photons.  Of course, three variables is a poor representation of a continuous function, but it's better than black and white which reduces light to just one variable, brightness.