# [GIF] Stepper (Two tessellations)

Posted 3 years ago
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| StepperThis is obviously the same basic idea as Reinvention, but with eight spokes rather than six.Two possibly confusing definitions in the following code: The quantity $r$ defines the length of the spokes, which varies between $1$ and $\sec(\pi/8) \approx 1.08239$. The latter is the length needed to make sure spokes connect in the quadrilaterals-and-octagons configuration, but leads to unpleasant visual artifacts if it isn't decreased to $1$ when switching configurations. The function $f(x)$ is $1$ minus $e^{-7x/16}\left[ \cos\left(\frac{3\sqrt{23}}{16}x\right) + \frac{1}{2} \sin \left(\frac{3\sqrt{23}}{16}x\right)\right]$, which is a solution of the (under-)damped harmonic oscillator equation $y'' + \frac{7}{8}y' +y=0$. Anyway, here's the code: DynamicModule[{n = 8, cols, f, t, r}, cols = RGBColor /@ {"#08D9D6", "#FF2E63", "#252A34"}; f[x_] := 1 - E^(-7 x/16) Cos[(3 Sqrt x)/16] - 1/2 E^(-7 x/16) Sin[(3 Sqrt x)/16]; Manipulate[ t = π/8 f[s] + π/8 f[Clip[s - 20, {0, 20}]]; r = (1 - f[s] + f[Clip[s - 20, {0, 20}]]) (1 - Sec[π/8]) + Sec[π/8]; Graphics[{Thickness[.01], CapForm["Round"], Table[Line[{x, 2 y + (-1)^x/2} + # & /@ {{0, 0}, r {Cos[θ + (-1)^x t], Sin[θ + (-1)^x t]}}, VertexColors -> {cols[], Blend[Join[#, #] &[cols[[;; 2]]], 1/3 f[s] + 1/3 f[Clip[s - 20, {0, 20}]]]}], {x, -3, 3}, {y, -3.25, 2.75}, {θ, 0, 2 π - 2 π/n, 2 π/n}]}, PlotRange -> 3, ImageSize -> 540, Background -> cols[]], {s, 0, 40}] ] Answer - another post of yours has been selected for the Staff Picks group, congratulations !We are happy to see you at the tops of the "Featured Contributor" board. Thank you for your wonderful contributions, and please keep them coming! Answer