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# Square root wave from sum of iterated sines

a guest Jan 12th, 2013 36 Never
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1. (*program start*)
2. Clear[x, y, n, a, xmin, xmax, ymin, ymax, c]
3. xmin = -1*Pi;
4. xmax = +3*Pi;
5. x = N[Range[xmin, xmax, 1/(50*Pi)], 90];
6. y1 = Sin[x];
7. y2 = Sin[y1];
8. y3 = Sin[y1 + y2];
9. y4 = Sin[y1 + y2 + y3];
10. y5 = Sin[y1 + y2 + y3 + y4];
11. y6 = Sin[y1 + y2 + y3 + y4 + y5];
12. y7 = Sin[y1 + y2 + y3 + y4 + y5 + y6];
13. y8 = Sin[y1 + y2 + y3 + y4 + y5 + y6 + y7];
14. y9 = Sin[y1 + y2 + y3 + y4 + y5 + y6 + y7 + y8];
15. y10 = Sin[y1 + y2 + y3 + y4 + y5 + y6 + y7 + y8 + y9];
16. y11 = Sin[y1 + y2 + y3 + y4 + y5 + y6 + y7 + y8 + y9 + y10];
17. y12 = Sin[y1 + y2 + y3 + y4 + y5 + y6 + y7 + y8 + y9 + y10 + y11];
18. y = y1 + y2 + y3 + y4 + y5 + y6 + y7 + y8 + y9 + y10 + y11 + y12;
19. Max[y]
20. a = Table[{x[[n]], y[[n]]}, {n, 1, Length[x]}];
21. a1 = Table[{x[[n]], y1[[n]]}, {n, 1, Length[x]}];
22. a2 = Table[{x[[n]], y2[[n]]}, {n, 1, Length[x]}];
23. a3 = Table[{x[[n]], y3[[n]]}, {n, 1, Length[x]}];
24. a4 = Table[{x[[n]], y4[[n]]}, {n, 1, Length[x]}];
25. a5 = Table[{x[[n]], y5[[n]]}, {n, 1, Length[x]}];
26. a6 = Table[{x[[n]], y6[[n]]}, {n, 1, Length[x]}];
27. a7 = Table[{x[[n]], y7[[n]]}, {n, 1, Length[x]}];
28. a8 = Table[{x[[n]], y8[[n]]}, {n, 1, Length[x]}];
29. a9 = Table[{x[[n]], y9[[n]]}, {n, 1, Length[x]}];
30. a10 = Table[{x[[n]], y10[[n]]}, {n, 1, Length[x]}];
31. a11 = Table[{x[[n]], y11[[n]]}, {n, 1, Length[x]}];
32. a12 = Table[{x[[n]], y12[[n]]}, {n, 1, Length[x]}];
33. ymin = Min[y]/Pi;
34. ymax = Max[y]/Pi;
35. ymin = -10/2*Pi;
36. ymax = 10/2*Pi;
37.
38. g = ListLinePlot[a,
39.    Ticks -> {Flatten[{xmin, xmax, Table[n, {n, xmin, xmax, Pi}]}],
40.      Flatten[{ymin, ymax, Table[k, {k, ymin, ymax, Pi}]}]},
41.    ImageSize -> Full, PlotRange -> {-Pi - 1/2, Pi + 1/2},
42.    PlotStyle -> RGBColor[1, 0, 1]];
43. g1 = ListLinePlot[a1,
44.    Ticks -> {Flatten[{xmin, xmax, Table[n, {n, xmin, xmax, Pi}]}],
45.      Flatten[{ymin, ymax, Table[k, {k, ymin, ymax, Pi}]}]},
46.    ImageSize -> Full, PlotRange -> {-Pi - 1/2, Pi + 1/2}];
47. g2 = ListLinePlot[a2,
48.    Ticks -> {Flatten[{xmin, xmax, Table[n, {n, xmin, xmax, Pi}]}],
49.      Flatten[{ymin, ymax, Table[k, {k, ymin, ymax, Pi}]}]},
50.    ImageSize -> Full, PlotRange -> {-Pi - 1/2, Pi + 1/2}];
51. g3 = ListLinePlot[a3,
52.    Ticks -> {Flatten[{xmin, xmax, Table[n, {n, xmin, xmax, Pi}]}],
53.      Flatten[{ymin, ymax, Table[k, {k, ymin, ymax, Pi}]}]},
54.    ImageSize -> Full, PlotRange -> {-Pi - 1/2, Pi + 1/2}];
55. g4 = ListLinePlot[a4,
56.    Ticks -> {Flatten[{xmin, xmax, Table[n, {n, xmin, xmax, Pi}]}],
57.      Flatten[{ymin, ymax, Table[k, {k, ymin, ymax, Pi}]}]},
58.    ImageSize -> Full, PlotRange -> {-Pi - 1/2, Pi + 1/2}];
59. g5 = ListLinePlot[a5,
60.    Ticks -> {Flatten[{xmin, xmax, Table[n, {n, xmin, xmax, Pi}]}],
61.      Flatten[{ymin, ymax, Table[k, {k, ymin, ymax, Pi}]}]},
62.    ImageSize -> Full, PlotRange -> {-Pi - 1/2, Pi + 1/2}];
63. g6 = ListLinePlot[a6,
64.    Ticks -> {Flatten[{xmin, xmax, Table[n, {n, xmin, xmax, Pi}]}],
65.      Flatten[{ymin, ymax, Table[k, {k, ymin, ymax, Pi}]}]},
66.    ImageSize -> Full, PlotRange -> {-Pi - 1/2, Pi + 1/2}];
67. g7 = ListLinePlot[a7,
68.    Ticks -> {Flatten[{xmin, xmax, Table[n, {n, xmin, xmax, Pi}]}],
69.      Flatten[{ymin, ymax, Table[k, {k, ymin, ymax, Pi}]}]},
70.    ImageSize -> Full, PlotRange -> {-Pi - 1/2, Pi + 1/2}];
71.
72. g8 = ListLinePlot[a8,
73.    Ticks -> {Flatten[{xmin, xmax, Table[n, {n, xmin, xmax, Pi}]}],
74.      Flatten[{ymin, ymax, Table[k, {k, ymin, ymax, Pi}]}]},
75.    ImageSize -> Full, PlotRange -> {-Pi - 1/2, Pi + 1/2}];
76.
77. g9 = ListLinePlot[a9,
78.    Ticks -> {Flatten[{xmin, xmax, Table[n, {n, xmin, xmax, Pi}]}],
79.      Flatten[{ymin, ymax, Table[k, {k, ymin, ymax, Pi}]}]},
80.    ImageSize -> Full, PlotRange -> {-Pi - 1/2, Pi + 1/2}];
81.
82. g10 = ListLinePlot[a10,
83.    Ticks -> {Flatten[{xmin, xmax, Table[n, {n, xmin, xmax, Pi}]}],
84.      Flatten[{ymin, ymax, Table[k, {k, ymin, ymax, Pi}]}]},
85.    ImageSize -> Full, PlotRange -> {-Pi - 1/2, Pi + 1/2}];
86.
87. g11 = ListLinePlot[a11,
88.    Ticks -> {Flatten[{xmin, xmax, Table[n, {n, xmin, xmax, Pi}]}],
89.      Flatten[{ymin, ymax, Table[k, {k, ymin, ymax, Pi}]}]},
90.    ImageSize -> Full, PlotRange -> {-Pi - 1/2, Pi + 1/2}];
91.
92. g12 = ListLinePlot[a12,
93.    Ticks -> {Flatten[{xmin, xmax, Table[n, {n, xmin, xmax, Pi}]}],
94.      Flatten[{ymin, ymax, Table[k, {k, ymin, ymax, Pi}]}]},
95.    ImageSize -> Full, PlotRange -> {-Pi - 1/2, Pi + 1/2}];
96.
97. Show[g, g1, g2, g3, g4, g5, g6, g7, g8, g9, g10, g11, g12]
98. (*program end*)
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