This graph was inspired by the (extensive) work on domain coloring by a member of the Desmos discord server (who I’ll name here, pending permission). The resulting diagram, when projected to the sphere, allows us to see the effect of the function over the entire input space! These colors are determined by the modulus (magnitude) and argument (angle) of the number when in polar form. Domain coloring works by assigning a color to each number in the complex plane, and moving each input to its output. Complex functions with one input and one output are 4-dimensional, so they’re non-trivial to visualize. Domain coloring is a method for visualizing complex functions. The Riemann Sphere is a model of the complex plane that uses inverse stereographic projection to fit the entire infinite plane onto a surface with finite surface area. Domain Coloring on the Riemann Sphere domain coloring on riemann sphere I’ll try to avoid graphs that I posted on YouTube. Nevertheless, here are eight of my favorites, in chronological order from oldest to newest. As such, attempting to comb through and select only a few graphs that represent the year is an exercise in futility. From harmonographs and obscure coordinate projections to artistic animations, this has probably been my most active year with Desmos, which is really saying something, since it has been my primary hobby for quite some time now. But it’s not 2023 yet (hours away!) so nobody can say I didn’t do it. In a Desmos Global Math Art Contest-induced fit of madness, I almost forgot to do the annual Desmos graph showcase.
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