Example 3. 300 Different Pseudocolor Schemes via One RGB Orthonormalization
Using matrix algebra, we can re-point the RGB color axes of the Schrödinger color cube in many possible directions to generate new color schemes. Consider (on a scale of 0 -1) that R, G, and B can take on three values each (0, 0.5, 1). With three channels, there are (3 x 3) - 1 = 8 nonzero possibilities. The number of ways to take eight things in three possible ways is 8!/(8-3)! = 8 x 7 x 6 = 336. However, 36 of these are singular. In Mathematica, we have explored all of these possibilities on the 'hotmap' pseudocolor scheme. Re-pointing the axes in 300 different ways can be accomplished, concisely, by taking allowed permutations of the (0, 0.5, 1) tuple. That generates a 3 x 3 matrix. Each value is then convolved with the hotmap by a dot product using a pseudoinverse. All 300 files are written out to an animated gif (3.1), shown below.
These colorbars are displayed in a Golden ratio of width and height, thus they look like an assembly of flags. Each can be used to index a monochrome (grayscale) image into a distinct pseudocolor space. Similarly, any other colorbar we construct (analogous to hotmap) can be taken through such an orthonormalization procedure to produce hundreds of daughter pseudocolor mappings.
Source code in .nb and .PDF formats. Each of these 300 pseudocoloring schemes is displayed individually in the PDF hyperlink to the fully executed code. It is not in the .nb format, because good image compression is needed to reduce file size.