What is the dimension of color ?

Think of color, pitch, loudness, heaviness, and hotness. Each is the topic of a branch of physics.

Benoit Mandelbrot

The prototypical fractal

( I'll continue with my 'watch notes' of the GEB series later this week. But I'll stay on topic with this post. )

Imagine a recursive process which goes to a certain depth until it stops. This 'certain depth' is a natural number which can be assigned a color. This is basically how fractals like the one above are built, pixel by pixel.

Programming 3D graphics can get quite realistic as we all know from watching movies or playing computer games. What is this reality? When does a picture look real to you? It is what made Rembrandt famous, I suppose. Control over light and thus color and shading.

What I am trying to say is that one number is not enough to encode a color. This is rather counter-intuitive, I know, but only if you assume the number of colors is finite or countable infinite. How many colors are there? Finitely many? Countable infinite many? Or not countable infinite? I don't know.

Assume a scene with an object with a certain color, say lime green. This can be coded with one string, the RGB color method uses 32 CD 32 ( Hex ) for lime green. But then you have an object that looks exactly the same everywhere. Because there is no light in the scene. By adding light we have to add the exact location of the light source in the scene. Shadows must be calculated. And light will be reflected. Each pixel will have a reflection vector which has effect on the color. Does this add to the dimension of the color? What if there are other objects in the scene? They partially reflect light and thus become a light source as well.

Do you get the idea? Then what is the dimension of ( the vector needed to encode a ) color?

More:
- The Dimensions of Colour