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Conformal neighborhoods of circles and subcircles. I.e. square grids that follow the curve. Square size depends on arc speed of underlying parameterization. Grid on one side of the curve is Schwarz reflection of grid on the other side, which here is inversion in the circle. 1/3pic.twitter.com/psAPCLRBgA
To compute these neighborhoods, find a conformal mapping that takes a real interval (or the entire real axis) to the circle, and then map the image of a grid containing the domain. (This of course can be generalized with maps to any curve) 2/3
Conformal mappings for the given pictures are normalized Jacobi sn, inverse stereoscopic, cos+i sin, and a frequency modulated version of cos+i sin. These were rendered in online Mathematica and have some artifacts. 3/3
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