Component and Complex Color Map Notes

The brightness/saturation and hue of a single pixel can be used to represent respectively the log[magnitude] and direction of a vector, or the log[amplitude] and phase of a complex number. Applications include for example strain mapping, wave & reciprocal space visualization, and vector geometry. In the process, some ideas (look out!) for 4-color decorating emerge as well.

A cyclic array of hues based on the three types of color sensors in the human eye looks like...

red, orange, yellow, chartreuse, green, seagreen, cyan, turquoise, blue, indigo, magenta, pink, red, etc.

If butterflies have four types of color sensor, how might their hue cycle differ? Would butterfly computer stores specialize in RGBU instead of RGB monitors? Did you hear about the recent (~May 2005) science news about butterfly usage of their ultraviolet sensors for global navigation?

Then there is the subject of color geometry...

The line between red and cyan makes right angles with that between chartreuse and indigo.

The line between blue and yellow is perpendicular to that between pink and seagreen.

The line between green and magenta is likewise orthogonal to that between turquoise and orange.

The horizontal rows show "spanning groups" of four colors, while the (approximate) vertical columns show "spanning groups" of three. I vote for indigo, seagreen, and orange. Should this be taken into account when, for example, choosing clothes, decorating a room, or deciding what colors to use in plotting graphs? Why do each of the orthogonal 4-color sets looks like a theme one might use to decorate a playroom? You may want to bookmark this page if just reading the sentences above makes you cheerful! On the other hand, would a business ensemble in such colors prevent folks at the office from being able to concentrate on their work? How about color themes restricted to only one quadrant? Might these colors help with someone's sense of focus, or for some might they instead exacerbate feelings of claustrophobia?

Note that the colors above are found only on the outside surface of the RGB color cube, as illustrated in the animation below of surfaces of varying chromaticity (HSL saturation). For a given value of satL, these align with the grayscale body-diagonal of the RGB cube. In this and other images to follow, the black lines are iso-contours of complex number amplitude and phase.

In addition to RGB, two other standard ways to parameterize color space are illustrated below. Note in particular that the HSL scheme maps all of these "complex/coordinate" colors onto a single layer of its hue and lightness manifold, leaving its color saturation or chromaticity manifold available as a third free parameter that one can store (along with amplitude and phase) in a single RGB image!

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