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Triangular wave partial sums of square wave recursion

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Jan 13th, 2013
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  1. (*program start*)Clear[x, y, n, a, xmin, xmax, ymin, ymax, c]
  2. xmin = -1*Pi;
  3. xmax = +5*Pi;
  4. x = N[Range[xmin, xmax, 1/(50*Pi)], 90];
  5. y1 = Sin[x];
  6. y2 = Sin[y1];
  7. y3 = Sin[y1 + y2];
  8. y4 = Sin[y1 + y2 + y3];
  9. y5 = Sin[y1 + y2 + y3 + y4];
  10. y6 = Sin[y1 + y2 + y3 + y4 + y5];
  11. y7 = Sin[y1 + y2 + y3 + y4 + y5 + y6];
  12. y8 = Sin[y1 + y2 + y3 + y4 + y5 + y6 + y7];
  13. y9 = Sin[y1 + y2 + y3 + y4 + y5 + y6 + y7 + y8];
  14. y10 = Sin[y1 + y2 + y3 + y4 + y5 + y6 + y7 + y8 + y9];
  15. y11 = Sin[y1 + y2 + y3 + y4 + y5 + y6 + y7 + y8 + y9 + y10];
  16. y12 = Sin[y1 + y2 + y3 + y4 + y5 + y6 + y7 + y8 + y9 + y10 + y11];
  17. y = y1 + y2 + y3 + y4 + y5 + y6 + y7 + y8 + y9 + y10 + y11 + y12;
  18. y1 = -Accumulate[y1];
  19. y2 = -Accumulate[y2];
  20. y3 = -Accumulate[y3];
  21. {
  22. {y4 = -Accumulate[y4];},
  23. {y5 = -Accumulate[y5];
  24. y6 = -Accumulate[y6];
  25. y7 = -Accumulate[y7];
  26. y8 = -Accumulate[y8];
  27. y9 = -Accumulate[y9];
  28. y10 = -Accumulate[y10];
  29. y11 = -Accumulate[y11];
  30. y12 = -Accumulate[y12];
  31. y = -Accumulate[y];
  32. yminmin = -600;
  33. ymaxmax = 550;}
  34. }
  35. Max[y];
  36. a = Table[{x[[n]], y[[n]]}, {n, 1, Length[x]}];
  37. a1 = Table[{x[[n]], y1[[n]]}, {n, 1, Length[x]}];
  38. a2 = Table[{x[[n]], y2[[n]] + y1[[n]]}, {n, 1, Length[x]}];
  39. a3 = Table[{x[[n]], y3[[n]] + y2[[n]] + y1[[n]]}, {n, 1, Length[x]}];
  40. a4 = Table[{x[[n]], y4[[n]] + y3[[n]] + y2[[n]] + y1[[n]]}, {n, 1,
  41. Length[x]}];
  42. a5 = Table[{x[[n]],
  43. y5[[n]] + y4[[n]] + y3[[n]] + y2[[n]] + y1[[n]]}, {n, 1,
  44. Length[x]}];
  45. a6 = Table[{x[[n]],
  46. y6[[n]] + y5[[n]] + y4[[n]] + y3[[n]] + y2[[n]] + y1[[n]]}, {n, 1,
  47. Length[x]}];
  48. a7 = Table[{x[[n]],
  49. y7[[n]] + y6[[n]] + y5[[n]] + y4[[n]] + y3[[n]] + y2[[n]] +
  50. y1[[n]]}, {n, 1, Length[x]}];
  51. a8 = Table[{x[[n]],
  52. y8[[n]] + y7[[n]] + y6[[n]] + y5[[n]] + y4[[n]] + y3[[n]] +
  53. y2[[n]] + y1[[n]]}, {n, 1, Length[x]}];
  54. a9 = Table[{x[[n]],
  55. y9[[n]] + y8[[n]] + y7[[n]] + y6[[n]] + y5[[n]] + y4[[n]] +
  56. y3[[n]] + y2[[n]] + y1[[n]]}, {n, 1, Length[x]}];
  57. a10 = Table[{x[[n]],
  58. y10[[n]] + y9[[n]] + y8[[n]] + y7[[n]] + y6[[n]] + y5[[n]] +
  59. y4[[n]] + y3[[n]] + y2[[n]] + y1[[n]]}, {n, 1, Length[x]}];
  60. a11 = Table[{x[[n]],
  61. y11[[n]] + y10[[n]] + y9[[n]] + y8[[n]] + y7[[n]] + y6[[n]] +
  62. y5[[n]] + y4[[n]] + y3[[n]] + y2[[n]] + y1[[n]]}, {n, 1,
  63. Length[x]}];
  64. a12 = Table[{x[[n]],
  65. y12[[n]] + y11[[n]] + y10[[n]] + y9[[n]] + y8[[n]] + y7[[n]] +
  66. y6[[n]] + y5[[n]] + y4[[n]] + y3[[n]] + y2[[n]] + y1[[n]]}, {n,
  67. 1, Length[x]}];
  68. ymin = Min[y]/Pi;
  69. ymax = Max[y]/Pi;
  70. ymin = -0 Pi;
  71. ymax = 0 Pi;
  72.  
  73. g = ListLinePlot[a,
  74. Ticks -> {Flatten[{xmin, xmax, Table[n, {n, xmin, xmax, Pi}]}],
  75. Flatten[{ymin, ymax, Table[k, {k, ymin, ymax, Pi}]}]},
  76. ImageSize -> Full, PlotRange -> {-Pi - 1/2, ymaxmax*Pi + 1/2},
  77. PlotStyle -> RGBColor[1, 0, 1]];
  78. g1 = ListLinePlot[a1,
  79. Ticks -> {Flatten[{xmin, xmax, Table[n, {n, xmin, xmax, Pi}]}],
  80. Flatten[{ymin, ymax, Table[k, {k, ymin, ymax, Pi}]}]},
  81. ImageSize -> Full, PlotRange -> {-Pi - 1/2, ymaxmax*Pi + 1/2}];
  82. g2 = ListLinePlot[a2,
  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, ymaxmax*Pi + 1/2}];
  86. g3 = ListLinePlot[a3,
  87. Ticks -> {Flatten[{xmin, xmax, Table[n, {n, xmin, xmax, Pi}]}],
  88. Flatten[{ymin, ymax, Table[k, {k, ymin, ymax, Pi}]}]},
  89. ImageSize -> Full, PlotRange -> {-Pi - 1/2, ymaxmax*Pi + 1/2}];
  90. g4 = ListLinePlot[a4,
  91. Ticks -> {Flatten[{xmin, xmax, Table[n, {n, xmin, xmax, Pi}]}],
  92. Flatten[{ymin, ymax, Table[k, {k, ymin, ymax, Pi}]}]},
  93. ImageSize -> Full, PlotRange -> {-Pi - 1/2, ymaxmax*Pi + 1/2}];
  94. g5 = ListLinePlot[a5,
  95. Ticks -> {Flatten[{xmin, xmax, Table[n, {n, xmin, xmax, Pi}]}],
  96. Flatten[{ymin, ymax, Table[k, {k, ymin, ymax, Pi}]}]},
  97. ImageSize -> Full, PlotRange -> {-Pi - 1/2, Pi + 1/2}];
  98. g6 = ListLinePlot[a6,
  99. Ticks -> {Flatten[{xmin, xmax, Table[n, {n, xmin, xmax, Pi}]}],
  100. Flatten[{ymin, ymax, Table[k, {k, ymin, ymax, Pi}]}]},
  101. ImageSize -> Full, PlotRange -> {-Pi - 1/2, ymaxmax*Pi + 1/2}];
  102. g7 = ListLinePlot[a7,
  103. Ticks -> {Flatten[{xmin, xmax, Table[n, {n, xmin, xmax, Pi}]}],
  104. Flatten[{ymin, ymax, Table[k, {k, ymin, ymax, Pi}]}]},
  105. ImageSize -> Full, PlotRange -> {-Pi - 1/2, ymaxmax*Pi + 1/2}];
  106.  
  107. g8 = ListLinePlot[a8,
  108. Ticks -> {Flatten[{xmin, xmax, Table[n, {n, xmin, xmax, Pi}]}],
  109. Flatten[{ymin, ymax, Table[k, {k, ymin, ymax, Pi}]}]},
  110. ImageSize -> Full, PlotRange -> {-Pi - 1/2, Pi + 1/2}];
  111.  
  112. g9 = ListLinePlot[a9,
  113. Ticks -> {Flatten[{xmin, xmax, Table[n, {n, xmin, xmax, Pi}]}],
  114. Flatten[{ymin, ymax, Table[k, {k, ymin, ymax, Pi}]}]},
  115. ImageSize -> Full, PlotRange -> {-Pi - 1/2, ymaxmax*Pi + 1/2}];
  116.  
  117. g10 = ListLinePlot[a10,
  118. Ticks -> {Flatten[{xmin, xmax, Table[n, {n, xmin, xmax, Pi}]}],
  119. Flatten[{ymin, ymax, Table[k, {k, ymin, ymax, Pi}]}]},
  120. ImageSize -> Full, PlotRange -> {-Pi - 1/2, ymaxmax*Pi + 1/2}];
  121.  
  122. g11 = ListLinePlot[a11,
  123. Ticks -> {Flatten[{xmin, xmax, Table[n, {n, xmin, xmax, Pi}]}],
  124. Flatten[{ymin, ymax, Table[k, {k, ymin, ymax, Pi}]}]},
  125. ImageSize -> Full, PlotRange -> {-Pi - 1/2, ymaxmax*Pi + 1/2}];
  126.  
  127. g12 = ListLinePlot[a12,
  128. Ticks -> {Flatten[{xmin, xmax, Table[n, {n, xmin, xmax, Pi}]}],
  129. Flatten[{ymin, ymax, Table[k, {k, ymin, ymax, Pi}]}]},
  130. ImageSize -> Full, PlotRange -> {-Pi - 1/2, ymaxmax*Pi + 1/2}];
  131.  
  132. Show[g, g1, g2, g3, g4, g5, g6, g7, g8, g9, g10, g11, g12,
  133. PlotRange -> {-Pi - 1/2, ymaxmax*Pi + 1/2}]
  134. (*program end*)
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