Can a printer print white color?

I was reading about different color models, when this question hit my mind.

Can the CMYK color model generate white color?

Printers use CMYK color mode. What will happen if I try to print a white colored image (rabbit) on a black paper with my printer? Will I get any image on the paper?

You will not get anything on the paper with a basic CMYK inkjet or laser printer. The CMYK color mixing is subtractive, meaning that it requires the base that is being colored to have all colors (i.e., White) So that it can create color variation through subtraction:

White - Cyan - Yellow = Green
White - Yellow - Magenta = Red
White - Cyan - Magenta = Blue

White is represented as 0 cyan, 0 yellow, 0 magenta, and 0 black - effectively, 0 ink for a printer that simply has those four cartridges. This works great when you have white media, as "printing no ink" simply leaves the white exposed, but as you can imagine, this doesn't work for non-white media.

If you don't have a base color to subtract from (i.e., Black), then it doesn't matter what you subtract from it, you still have the color Black.

As others are pointing out, there are special printers which can operate in the CMYW color space, or otherwise have a white ink or toner. These can be used to print light colors on top of dark or otherwise non-white media.

You might also find my answer to a different question about color spaces helpful or informative.

It depends on the printer. If it's an inkjet printer, the mixture of these colors will just soak into the black paper. It will be much like using a dark colored marker pen on black paper.

With a laser printer, it's different, because it works by depositing a plastic powder on top of the paper, and melting it on, like the toppings of a pizza.

This property of the laser printer method makes it possible to do toner transfers: to print something onto transfer paper, and then transfer the toner from the paper onto an object. I have etched circuit boards this way, by transferring toner to copper, that toner being thick enough to resist the etching solution.

Colored toner baked onto dark paper should therefore be visible, but no combination of the toner colors will produce white.

The Japanese company ALPS produced a printing technology which could render unusual colors, like white.