Domain Coloring Windows
Another visualization technique employed for complex functions of one
variable is "domain coloring." The basic idea is to use color to convey information about the function. The
following is "pseudo-code" for the technique:
- for each point
p in the domain:
- calculate f(p)
- assign a
color (R,G,B) according to the value of f(p)
- Use (R,G,B) to
color p
The tricky part lies in choosing mapping from the complex plane to (R,G,B)
color-space. Frank Farris, a
Mathematics Professor at Santa Clara University, has proposed a
color-assignment method quite similar to the traditional color wheel.
Hue varies as the angle changes, while saturation varies with the modulus.
Prof. Farris uses a division of 12 separate hues, interpolated from the
three primary colors located at the three fundamental roots of unity.
Zeroes of complex functions are represented as pure-white, while poles are
black.
g(z) employs the same general principle, but
uses an HSV color wheel, providing a continuous blending of colors and
saturations: