Post #2704905

#Polyhedron #Polygons #tiles #opticalillusion #MathArt #MathsArt The visible spectrum is a line segment in frequency space for light. It is naturally embedded in 4 edges of the hue hexagon. This is shown in the previous figure. We let the frequency of monochromatic light, \(\nu\), vary across the visible spectrum to get the curve. Its image is the 4 edges from \((1,0,0)\) to \((0,0,1)\). This is the spectral locus in the color cube. The remaining 2 edges is the "line" of purples, the hues that do not correspond to monochromatic light. They are stimulated by mixtures of red and violet light. The complement of a hue is the hue it has to be mixed with to get a completely desaturated color. The antipodal points on the surface of the color cube are pairs of complementary colors. Antipodal points on the hue hexagon are pairs of complementary colors. The primary and secondary hues form 3 pairs of complementary hues. Proceeding with the analogy, there are four cones in tetrachromatic vision. To implement Ooqui's "rule of hue" their spectral sensitivity curves are again idealized to piecewise linear functions shown in the figure. Call them \(\chi_1(\nu)\), \(\chi_2(\nu)\), \(\chi_3(\nu)\), and \(\chi_4(\nu)\). They are surjective to \([0,1]\). Again, each cone type has exactly 1 frequency where it is the only type of cone that is activated and that cone's activation is 1 at that frequency. These frequencies are 415, 515, 615, and 715. At every other frequency exactly 2 cone types are activated and the activation of at least one of them is 1. The set of all tetrachromatic colors is the color tesseract \([0,1]^4\). (3/6)