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What am I looking at?

The image you see are geodesics on a Poincaré (pwawn-car-eh) disk. Specifically, the curves shown appear bifurcated along a diagonal bisector of the circular boundary. In fact, this bisector, rotated 35.2° counterclockwise from the horizontal, gives us a pair of antipodal points on this circle that we define our geodesics about. The curves seen emerge from these antipodal points as circular arcs and terminate at the disk’s boundary. The arcs that unfurl from the upper right point connect to the boundary above the bisector, while the arcs below the boundary stem from the lower left point. Dashed lines are used instead of solid lines resulting in a quasi-moiré pattern forming that contrasts against the bend of the geodesics. Diametric tones are used in the two colors gradients of the upper and lower geodesics which converge to a shared hue at the bisector. All of this culminates in a neon, taijitu-inspired geometric symbol whose curves seemingly repel each other while the gaps between them oppose this repulsion and appear attractive. This image can be referred to or referenced as the Poincaré Taijitu.

  1. Poincaré Taijitu © 2024 by David J. Gillcrist is licensed under Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International ↩︎