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#Polyhedron #Polygons #tiles #opticalillusion #MathArt #MathsArt

The video in this post by @graveolensa

https://mathstodon.xyz/@graveolensa/115885487505867437

about people with 4 color cones having a sphere's worth of hues is fascinating but, being a trichromat, i don't fully understand it or know if its correct. Here is a mathematically simple but scientifically crude analogy between trichromaticity and tetrachromaticity.

A note on the figures, although this is about color vision and the figures have been colored the colors in the figures are just rough guides for trichromats, which most people are. This analogy is too crude for the colors to precisely match a trichromat's color experiences.

The visible spectrum is rounded off to the interval [415 THz, 715 THz]. The cone cells' activation, as a function of the frequency of monochromatic light they receive, are idealized to the piecewise linear spectral sensitivity curves shown in the figure. They are surjective to \([0,1]\) so as to implement Ooqui's "rule of hue". Call them \(r(\nu)\) (red cone), \(g(\nu)\) (green cone), and \(b(\nu)\) (violet cone).

Each cone type has exactly 1 frequency of monochromatic light 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, 565, and 715. At every other frequency in the visible spectrum exactly 2 cone types are activated by monochromatic light and the activation of at least one of them is 1.

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