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5

Use Table old[τ_] := Sin[τ] new[α_, χ_, τ_] := Sin[α τ]^2 + Cos[χ τ]^2 result = Table[Plot3D[ new[α, χ, τ] - old[τ], {α, 0, 2 π}, {χ, 0, π}, MaxRecursion -> 0, AxesLabel -> Automatic] , {τ, 1/10, 1, 1/10}] Export["result.gif", result] Or use Animate Animate[Plot3D[ new[α, χ, τ] - old[τ], {α, 0, 2 π}, {χ, 0, π}, MaxRecursion -> 0, ...

4

Using custom Arrowheads (instead of Epilog) may be slightly more flexible: ah1 = Arrowheads[{{-0.05}, {0.015, 1, Graphics@{EdgeForm[Blue], White, Disk[]}}}]; ah2 = Arrowheads[{{0.05, 1}, {0.015, 0, Graphics@ Disk[]}}]; pw = Piecewise[{{-x^2, x < 1}, {x + 1, x >= 1}}]; This can be used with a combination of MeshFunctions and MeshShading: Plot[pw, {...

3

Just for fun, here is a variation of C. E.'s animation, which demonstrates that an epicycloid can be constructed as an envelope of the diameter of a rolling circle: With[{n = 3, r = 1, m = 31}, Animate[ParametricPlot[ReIm[(n + 1) r E^(I t) - r E^(I (n + 1) t)], {t, 0, 2 π}, Axes -> None, ...

1

Use Part to subtract intensity and Transpose to align with the wavelength data: wavelength = Range[350, 750, (400/3647)]; withMagnet = Transpose[{wavelength, RandomReal[1, 3648]}]; withoutMagnet = Transpose[{wavelength, RandomReal[1, 3648]}]; (*The above code just simulates your imported data*) diff = Transpose[{withoutMagnet[[All, 1]], ...

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