Rendering of environment by a computer is something that we encounter more and more often, especially in computer games and movies. Assigning colors to regions is an important part of this process (we actually teach it at our faculty) and it is based on mathematics (naturally). One of the basic tools is matematical coloring functions. The idea is simple: If we want to know how to color some point, then we just substitute its coordinates to the coloring function and the resulting value decides on the right color.
You can try it out in our mathematical coloring book. All coloring pictures come in two versions. The basic version includes a key hint. It should be accessible by high-school students, and in fact it is a pleasant practice of working with Carthesian and polar coordinates. You can solve it on paper, but we also offer an interactive online interface.
The more adventurous users can try the full version, which requires some work with functions and equations and basic working knowledge of analytic geometry. A university freshman should be able to handle it, but it could be also an interesting challenge for ambitious high-school students. These hardcore versions were sorted by difficulty. These full versions differ in difficulty that we marked in the links, and they have to be solved on paper (you can print them). Warning: If you are thinking of trying some picture in full version, then definitely do not look at the basic version as the hint there would spoil all the fun.
Everything is explained in these instructions.
Pictures based on Carthesian coordinates.
| Warm colors basic full (easy) |
Contrast basic full (easy) |
Man overboard basic full (easy) |
Landscape basic full (easy) |
House basic full (easy) |
| Spectrum basic full (intermediate) |
Diagonals basic full (intermediate) |
All about red basic full (intermediate) |
Tablecloth basic full (intermediate) |
Chess basic full (intermediate) |
| Private basic full (intermediate) |
Rays basic full (intermediate) |
Sea basic full (intermediate) |
Tunnel basic full (tougher) |
| Colors basic full (tougher) |
Spring basic full (tougher) |
Blues basic full (tougher) |
Cross basic full (tougher) |
In the sea basic full (tougher) |
Pictures based on polar coordinates.
| Rainbow basic full (easy) |
Pie basic full (easy) |
Flag basic full (easy) |
Yin/Yang basic full (intermediate) |
| Pac-Man basic full (intermediate) |
Bud basic full (intermediate) |
Baby carriage basic full (intermediate) |
Bullseye basic full (tougher) |
Dawn basic full (tougher) |