# [GIF] This is Only a Test (Decagons from stereographic projections)

Posted 1 year ago
1733 Views
|
|
5 Total Likes
|
 This is Only a TestThis one is fairly straightforward. Form 60 concentric circles on the sphere centered at the point $(0,1,0)$. On each circle, take 10 equally-spaced points, stereographically project to the plane, and form a decagon from the resulting points. Now rotate the sphere and all the points on it around the axis $(0,1,0)$. The result (at least after adding some color) is this animation. This is a sort of discretized companion to my old still piece Dipole.Here's the code: Stereo[p_] := p[[;; -2]]/(1 - p[[-1]]); With[{r = 2, n = 10, m = 60, cols = RGBColor /@ {"#2EC4B6", "#011627", "#E71D36"}}, Manipulate[ Graphics[ {EdgeForm[Thickness[.0045]], Join[{Reverse[#[[1]]], #[[2]]}] &[Partition[ Table[ {Blend[cols, θ/π], EdgeForm[Lighter[Blend[cols, θ/π], .15]], Polygon[ Table[Stereo[(Cos[θ] {0, 1, 0} + Sin[θ] {Cos[t], 0, Sin[t]}).RotationMatrix[ϕ, {0, 1, 0}]], {t, π/2, 5 π/2, 2 π/n}]]}, {θ, π/(2 m), π - π/(2 m), π/m}], m/2]]}, PlotRange -> r, ImageSize -> 540, Background -> Blend[cols, 1/2]], {ϕ, 0, 2 π/n}] ]