File:Sequential superposition of plane waves.gif

Summary

made in Mathematica with the following sloppy but effective code: Do[a[jj] =

  Plot[{Cos[x], Cos[2 x] + 10 - 0.25*jj}, {x, -Pi, Pi}, 
   PlotRange -> {-3, 12}, Axes -> {True, False}, 
   Ticks -> False], {jj, 1, 40}];

Do[a[jj] =

  Plot[{Cos[x] + 0.1*(jj - 40)*Cos[2 x], 
    0.1*(50 - jj)*Cos[2 x]}, {x, -Pi, Pi}, PlotRange -> {-3, 12}, 
   Axes -> {True, False}, Ticks -> False], {jj, 41, 50}];

Do[a[jj] =

  Plot[{Cos[x] + Cos[2 x], Cos[3 x] + 10 - 0.25*(jj - 50)}, {x, -Pi, 
    Pi}, PlotRange -> {-3, 12}, Axes -> {True, False}, 
   Ticks -> False], {jj, 51, 90}];

Do[a[jj] =

  Plot[{Cos[x] + Cos[2 x] + 0.1*(jj - 90)*Cos[3 x], 
    0.1*(100 - jj)*Cos[3 x]}, {x, -Pi, Pi}, PlotRange -> {-3, 12}, 
   Axes -> {True, False}, Ticks -> False], {jj, 91, 100}];

Do[a[jj] =

  Plot[{Cos[x] + Cos[2 x] + Cos[3 x], 
    Cos[4 x] + 10 - 0.25*(jj - 100)}, {x, -Pi, Pi}, 
   PlotRange -> {-3, 12}, Axes -> {True, False}, 
   Ticks -> False], {jj, 101, 140}];

Do[a[jj] =

  Plot[{Cos[x] + Cos[2 x] + Cos[3 x] + 0.1*(jj - 140)*Cos[4 x], 
    0.1*(150 - jj)*Cos[4 x]}, {x, -Pi, Pi}, PlotRange -> {-3, 12}, 
   Axes -> {True, False}, Ticks -> False], {jj, 141, 150}];

Do[a[jj] =

  Plot[{Cos[x] + Cos[2 x] + Cos[3 x] + Cos[4 x], 
    Cos[5 x] + 10 - 0.25*(jj - 150)}, {x, -Pi, Pi}, 
   PlotRange -> {-3, 12}, Axes -> {True, False}, 
   Ticks -> False], {jj, 151, 190}];

Do[a[jj] =

  Plot[{Cos[x] + Cos[2 x] + Cos[3 x] + Cos[4 x] + 
     0.1*(jj - 190)*Cos[5 x], 0.1*(200 - jj)*Cos[5 x]}, {x, -Pi, Pi},
    PlotRange -> {-3, 12}, Axes -> {True, False}, 
   Ticks -> False], {jj, 191, 200}];

Do[a[jj] =

  Plot[{Cos[x] + Cos[2 x] + Cos[3 x] + Cos[4 x] + Cos[5 x], 
    Cos[6 x] + 10 - 0.25*(jj - 200)}, {x, -Pi, Pi}, 
   PlotRange -> {-3, 12}, Axes -> {True, False}, 
   Ticks -> False], {jj, 201, 240}];

Do[a[jj] =

  Plot[{Cos[x] + Cos[2 x] + Cos[3 x] + Cos[4 x] + Cos[5 x] + 
     0.1*(jj - 240)*Cos[6 x], 0.1*(250 - jj)*Cos[6 x]}, {x, -Pi, Pi},
    PlotRange -> {-3, 12}, Axes -> {True, False}, 
   Ticks -> False], {jj, 241, 250}];

Do[a[jj] =

  Plot[{Cos[x] + Cos[2 x] + Cos[3 x] + Cos[4 x] + Cos[5 x] + 
     Cos[6 x], Cos[7 x] + 10 - 0.25*(jj - 250)}, {x, -Pi, Pi}, 
   PlotRange -> {-3, 12}, Axes -> {True, False}, 
   Ticks -> False], {jj, 251, 290}];

Do[a[jj] =

  Plot[{Cos[x] + Cos[2 x] + Cos[3 x] + Cos[4 x] + Cos[5 x] + 
     Cos[6 x] + 0.1*(jj - 290)*Cos[7 x], 
    0.1*(300 - jj)*Cos[7 x]}, {x, -Pi, Pi}, PlotRange -> {-3, 12}, 
   Axes -> {True, False}, Ticks -> False], {jj, 291, 300}];

Do[a[jj] =

  Plot[{Cos[x] + Cos[2 x] + Cos[3 x] + Cos[4 x] + Cos[5 x] + 
     Cos[6 x] + Cos[7 x], Cos[8 x] + 10 - 0.25*(jj - 300)}, {x, -Pi, 
    Pi}, PlotRange -> {-3, 12}, Axes -> {True, False}, 
   Ticks -> False], {jj, 301, 340}];

Do[a[jj] =

  Plot[{Cos[x] + Cos[2 x] + Cos[3 x] + Cos[4 x] + Cos[5 x] + 
     Cos[6 x] + Cos[7 x] + 0.1*(jj - 340)*Cos[8 x], 
    0.1*(350 - jj)*Cos[8 x]}, {x, -Pi, Pi}, PlotRange -> {-3, 12}, 
   Axes -> {True, False}, Ticks -> False], {jj, 341, 350}];

Do[a[jj] =

  Plot[{Cos[x] + Cos[2 x] + Cos[3 x] + Cos[4 x] + Cos[5 x] + 
     Cos[6 x] + Cos[7 x] + Cos[8 x], 
    Cos[9 x] + 10 - 0.25*(jj - 350)}, {x, -Pi, Pi}, 
   PlotRange -> {-3, 12}, Axes -> {True, False}, 
   Ticks -> False], {jj, 351, 390}];

Do[a[jj] =

  Plot[{Cos[x] + Cos[2 x] + Cos[3 x] + Cos[4 x] + Cos[5 x] + 
     Cos[6 x] + Cos[7 x] + Cos[8 x] + 0.1*(jj - 390)*Cos[9 x], 
    0.1*(400 - jj)*Cos[9 x]}, {x, -Pi, Pi}, PlotRange -> {-3, 12}, 
   Axes -> {True, False}, Ticks -> False], {jj, 391, 400}];

Do[a[jj] =

  Plot[{Cos[x] + Cos[2 x] + Cos[3 x] + Cos[4 x] + Cos[5 x] + 
     Cos[6 x] + Cos[7 x] + Cos[8 x] + Cos[9 x], 
    Cos[10 x] + 10 - 0.25*(jj - 400)}, {x, -Pi, Pi}, 
   PlotRange -> {-3, 12}, Axes -> {True, False}, 
   Ticks -> False], {jj, 401, 440}];

Do[a[jj] =

  Plot[{Cos[x] + Cos[2 x] + Cos[3 x] + Cos[4 x] + Cos[5 x] + 
     Cos[6 x] + Cos[7 x] + Cos[8 x] + Cos[9 x] + 
     0.1*(jj - 440)*Cos[10 x], 0.1*(450 - jj)*Cos[10 x]}, {x, -Pi, 
    Pi}, PlotRange -> {-3, 12}, Axes -> {True, False}, 
   Ticks -> False], {jj, 441, 450}];

frames = ParallelTable[a[jj], {jj, 0, 450}];

Licensing

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