[GIF] Dig In (Stereographic image of concentric circles)

Posted 1 year ago
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 Dig InSimilar to Interference: in this case, I'm just taking the stereographic images of concentric circles centered at $(0,0,1)$ on the sphere. It's a simple calculation to see that the circle of (spherical) radius $r$ centered at the north pole is mapped by stereographic projection to a circle of radius $\frac{\sin r}{1-\cos r}$ in the plane, so those are the circles actually shown in the animation.Here's the code: DynamicModule[{cols = {White, Black}, n = 48}, Manipulate[ Graphics[{cols[[1]], Thickness[.002], Table[{Hue[(r + s)/(2 π) + .3], Opacity[.2 (1 - Cos[r + s])], Disk[{0, 0}, Sin[r + s]/(1 - Cos[r + s])]}, {s, π/n, π, π/n}]}, PlotRange -> 3, ImageSize -> 540, Axes -> None, Background -> cols[[-1]]], {r, 0., -π/n - #, #}] &[-π/(40 n)] ]