# Experimenting with fun curve plots from Wolfram Alpha

Posted 10 years ago
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 Hello all...Recently I ran across a link to some fun plotting with Wolfram Alpha (WA). It uses the following syntax more-or-less: "Graph a x curve", where "x" is some object --- tree, curious george, dragon, etc. It's fun to play with; at least I think so!http://www.wolframalpha.com/input/?i=Graph+a+tree+curveWhat I thought would be straight-forward turned out not to be (for me).I thought about copying the equatons given by WA and using them in a Mathematica (v. 8) notebook for further experimentation. Problem is, I'm not able to get the plot to show up without many errors. I'm still in the rudimentary stages with the software (I don't get the time with it due to other priorities). The 'help' is usually pretty good, but I'm not 'getting it' I guess.How do you port the WA output into a Mathematica Notebook to reproduce the plot?Thank you.
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Posted 10 years ago
 Hello   Himura Kazuto....Well....I am quite embarrassed! These are things I should have known, or seen. I looked  other things, and how I mised these, well, all I can say is, my mind must be tainted from a class I'm taking that involves using Mathcad.Everything you said makes sense, and it works perfectly. I appreciate your kind help, thank you so much.Wishing you all the best.To Vitaliy Kaurov...I thank you as well for your excellent help!
Posted 10 years ago
 There are many ways to get the pure formula. Read these blogs to understand how:Making Formulas for EverythingFrom Pi to the Pink Panther to Sir Isaac NewtonEven More Formulas for EverythingFrom Filled Algebraic Curves to the Twitter Bird, the American Flag, Chocolate Easter Bunnies, and the Superman SolidMaking Formulas for EverythingFrom Pi to the Pink Panther to Sir Isaac Newton{x[t_], y[t_]} = WolframAlpha["tree curve", {{"EquationsPod:PopularCurveData", 1}, "FormulaData"}][[All, 1]][[All, 2]];ParametricPlot[{x[t], y[t]}, {t, 0, 2 Pi}, Axes -> False]
Posted 10 years ago
 You should make the syntax compareble. Use Auto-Replace of your favourite plain-text editor (AkelPad is mine).Do the folowing replaces:"(" -> "["")" -> "]""sin " ->"Sin"and define the functions as f[x_] := Take your tree =)  x[t_] := -2/3 Sin[11/8 - 256 t] - 4/11 Sin[1/4 - 235 t] -     2/7 Sin[1/3 - 234 t] - 1/7 Sin[5/7 - 232 t] -     1/2 Sin[11/12 - 227 t] - 3/4 Sin[1/5 - 220 t] - Sin[2/3 - 216 t] -     10/7 Sin[1/11 - 215 t] - 1/2 Sin[3/7 - 212 t] -     1/3 Sin[3/4 - 206 t] - 11/7 Sin[2/7 - 187 t] -     5/6 Sin[1/4 - 183 t] - 7/5 Sin[5/6 - 180 t] -     4/3 Sin[11/9 - 176 t] - 3/8 Sin[3/4 - 174 t] -     20/13 Sin[1/5 - 173 t] - 2 Sin[4/7 - 171 t] -     28/27 Sin[5/4 - 167 t] - 17/11 Sin[5/4 - 163 t] -    20/13 Sin[3/5 - 161 t] - 5/3 Sin[1 - 156 t] -    11/8 Sin[16/11 - 154 t] - 19/6 Sin[5/7 - 152 t] -    13/8 Sin[6/7 - 145 t] - 22/7 Sin[7/6 - 142 t] -    21/10 Sin[1/17 - 141 t] - 11/12 Sin[13/12 - 137 t] -    18/7 Sin[13/10 - 136 t] - 5/4 Sin[2/3 - 135 t] -    29/8 Sin[8/7 - 123 t] - 3/8 Sin[1/6 - 120 t] -    17/16 Sin[3/7 - 110 t] - 2 Sin[13/12 - 109 t] -    8/5 Sin[14/9 - 104 t] - 11/4 Sin[10/11 - 88 t] -    5/7 Sin[11/8 - 79 t] - 7/6 Sin[14/13 - 78 t] -    23/7 Sin[11/8 - 77 t] - 12/7 Sin[21/20 - 74 t] -    14/9 Sin[1/7 - 73 t] - 30/31 Sin[14/15 - 63 t] -    19/6 Sin[23/24 - 60 t] - 22/5 Sin[1/11 - 59 t] -    9/2 Sin[3/10 - 52 t] - 26/3 Sin[7/6 - 50 t] -    76/17 Sin[2/5 - 47 t] - 41/9 Sin[13/9 - 40 t] -    90/13 Sin[1/17 - 33 t] - 607/38 Sin[2/7 - 31 t] -    151/10 Sin[3/5 - 25 t] - 18 Sin[1 - 24 t] -    383/12 Sin[7/13 - 12 t] - 29 Sin[7/6 - 11 t] -    335/11 Sin[10/7 - 10 t] - 140/3 Sin[5/6 - 9 t] -    755/8 Sin[7/5 - 2 t] - 2675/6 Sin[5/6 - t] + 27/7 Sin[132 t] +    5/11 Sin[245 t] + 345/7 Sin[3 t + 14/3] + 2753/32 Sin[4 t + 27/8] +    533/6 Sin[5 t + 10/7] + 1177/21 Sin[6 t + 5/8] +    319/13 Sin[7 t + 5/8] + 81/4 Sin[8 t + 7/5] +    101/5 Sin[13 t + 17/5] + 149/5 Sin[14 t + 25/6] +    37/7 Sin[15 t + 31/8] + 1059/23 Sin[16 t + 19/5] +    97/6 Sin[17 t + 109/36] + 89/6 Sin[18 t + 8/5] +    436/29 Sin[19 t + 18/7] + 149/8 Sin[20 t + 7/11] +    33/2 Sin[21 t + 12/7] + 113/6 Sin[22 t + 1/9] +    80/3 Sin[23 t + 2/7] + 181/11 Sin[26 t + 16/7] +    151/8 Sin[27 t + 17/11] + 41/7 Sin[28 t + 17/6] +    44/9 Sin[29 t + 20/7] + 39/4 Sin[30 t + 8/5] +    39/10 Sin[32 t + 40/11] + 53/10 Sin[34 t + 17/4] +    63/5 Sin[35 t + 29/8] + 16/5 Sin[36 t + 6/5] +    111/10 Sin[37 t + 80/27] + 67/17 Sin[38 t + 19/7] +    29/15 Sin[39 t + 4] + 11/3 Sin[41 t + 23/8] +    109/9 Sin[42 t + 20/9] + 13/3 Sin[43 t + 31/9] +    21/11 Sin[44 t + 31/9] + 23/6 Sin[45 t + 17/7] +    23/3 Sin[46 t + 5/4] + 19/13 Sin[48 t + 9/7] +    21/8 Sin[49 t + 2/5] + 13/5 Sin[51 t + 21/5] +    9/5 Sin[53 t + 34/9] + 25/6 Sin[54 t + 13/7] +    7/8 Sin[55 t + 51/26] + 15/8 Sin[56 t + 24/7] +    7/2 Sin[57 t + 7/6] + 7/5 Sin[58 t + 23/8] +    11/5 Sin[61 t + 33/7] + 22/5 Sin[62 t + 17/7] + 7/3 Sin[64 t + 3] +    17/5 Sin[65 t + 11/5] + 7/3 Sin[66 t + 70/23] +    11/3 Sin[67 t + 15/16] + 17/7 Sin[68 t + 6/7] +    35/9 Sin[69 t + 23/8] + 129/32 Sin[70 t + 12/5] +    13/5 Sin[71 t + 30/7] + 10/7 Sin[72 t + 19/9] +    13/6 Sin[75 t + 11/9] + 16/11 Sin[76 t + 18/7] +    9/5 Sin[80 t + 6/5] + 4/9 Sin[81 t + 8/5] + 13/6 Sin[82 t + 1/14] +    35/8 Sin[83 t + 11/9] + 13/4 Sin[84 t + 2/9] +    32/11 Sin[85 t + 29/10] + Sin[86 t + 5/4] + 18/7 Sin[87 t + 1/5] +    17/10 Sin[89 t + 11/6] + 9/10 Sin[90 t + 17/7] +    19/7 Sin[91 t + 16/15] + 4/7 Sin[92 t + 29/7] +    57/28 Sin[93 t + 12/11] + 26/7 Sin[94 t + 3/2] +    11/8 Sin[95 t + 4/3] + 10/3 Sin[96 t + 19/10] +    8/5 Sin[97 t + 5/3] + 22/9 Sin[98 t + 39/10] +    27/14 Sin[99 t + 9/7] + 12/7 Sin[100 t + 27/8] +    40/9 Sin[101 t + 97/32] + 3/7 Sin[102 t + 53/27] +    8/5 Sin[103 t + 11/9] + 34/11 Sin[105 t + 4] +    1/2 Sin[106 t + 11/6] + 5/9 Sin[107 t + 25/12] +    19/9 Sin[108 t + 11/6] + 13/8 Sin[111 t + 7/2] +    5/2 Sin[112 t + 1/5] + 14/5 Sin[113 t + 5/2] +    21/5 Sin[114 t + 2/5] + 49/9 Sin[115 t + 44/15] +    13/5 Sin[116 t + 11/4] + 5/8 Sin[117 t + 11/3] +    23/8 Sin[118 t + 21/5] + 16/5 Sin[119 t + 35/9] +    13/9 Sin[121 t + 2/7] + 7/13 Sin[122 t + 5/3] +    11/4 Sin[124 t + 3/2] + 11/7 Sin[125 t + 17/5] +    3/5 Sin[126 t + 2/3] + 10/9 Sin[127 t + 88/29] +    9/5 Sin[128 t + 11/3] + 15/8 Sin[129 t + 5/6] +    17/10 Sin[130 t + 46/13] + 9/4 Sin[131 t + 15/4] +    5/2 Sin[133 t + 2] + 43/14 Sin[134 t + 13/7] +    9/7 Sin[138 t + 16/7] + 5/3 Sin[139 t + 5/3] +    4/7 Sin[140 t + 10/3] + 25/12 Sin[143 t + 4/5] +    12/5 Sin[144 t + 7/5] + 3/2 Sin[146 t + 13/10] +    19/10 Sin[147 t + 2/3] + 23/8 Sin[148 t + 3] +    8/3 Sin[149 t + 1/8] + 43/22 Sin[150 t + 32/9] +    12/7 Sin[151 t + 21/8] + 5/6 Sin[153 t + 9/2] +    11/7 Sin[155 t + 6/5] + 4/3 Sin[157 t + 6/5] + 5/8 Sin[158 t + 4] +    8/9 Sin[159 t + 10/7] + 15/16 Sin[160 t + 5/2] +    6/7 Sin[162 t + 11/7] + 2/3 Sin[164 t + 11/5] +    5/11 Sin[165 t + 17/10] + 11/3 Sin[166 t + 26/11] +    6/5 Sin[168 t + 67/15] + 3/4 Sin[169 t + 1/7] +    38/13 Sin[170 t + 19/7] + Sin[172 t + 137/34] +    17/9 Sin[175 t + 13/4] + 7/4 Sin[177 t + 3/10] +    5/6 Sin[178 t + 22/21] + 10/9 Sin[179 t + 9/2] +    12/7 Sin[181 t + 4/7] + 10/9 Sin[182 t + 9/5] +    5/6 Sin[184 t + 13/6] + 4/9 Sin[185 t + 18/7] +    1/2 Sin[186 t + 19/8] + 1/4 Sin[188 t + 28/11] +    3/5 Sin[189 t + 43/10] + 9/7 Sin[190 t + 7/3] +    2/7 Sin[191 t + 19/7] + 5/7 Sin[192 t + 7/5] +    3/5 Sin[193 t + 23/7] + 7/13 Sin[194 t + 1/5] +   11/8 Sin[195 t + 18/7] + 6/7 Sin[196 t + 11/3] +   1/2 Sin[197 t + 16/17] + 12/11 Sin[198 t + 3/7] +   3/5 Sin[199 t + 13/6] + 3/5 Sin[200 t + 23/6] +   5/7 Sin[201 t + 5/6] + 19/20 Sin[202 t + 40/11] +   3/4 Sin[203 t + 19/8] + 11/12 Sin[204 t + 9/7] +   22/21 Sin[205 t + 9/10] + 2/7 Sin[207 t + 52/17] +   3/7 Sin[208 t + 20/7] + 7/6 Sin[209 t + 1/6] +   6/13 Sin[210 t + 7/3] + 4/3 Sin[211 t + 12/5] +   7/9 Sin[213 t + 10/3] + 5/4 Sin[214 t + 41/10] +   2/3 Sin[217 t + 16/9] + 7/8 Sin[218 t + 12/5] +   2/3 Sin[219 t + 23/7] + 5/4 Sin[221 t + 53/18] +   33/32 Sin[222 t + 4/5] + 5/4 Sin[223 t + 35/8] +   5/8 Sin[224 t + 3] + 5/8 Sin[225 t + 3] + 2/7 Sin[226 t + 21/5] +   1/9 Sin[228 t + 24/7] + 1/7 Sin[229 t + 53/26] +   9/8 Sin[230 t + 18/5] + 6/5 Sin[231 t + 17/5] +   17/16 Sin[233 t + 9/8] + 3/10 Sin[236 t + 16/9] +   7/10 Sin[237 t + 25/7] + 6/5 Sin[238 t + 17/7] +   5/11 Sin[239 t + 15/8] + 2/9 Sin[240 t + 3/8] +   3/7 Sin[241 t + 11/3] + 1/3 Sin[242 t + 154/51] +   4/7 Sin[243 t + 8/3] + Sin[244 t + 17/6] + 7/6 Sin[246 t + 32/9] +   1/7 Sin[247 t + 58/19] + 4/5 Sin[248 t + 7/8] +   1/23 Sin[249 t + 12/5] + 5/7 Sin[250 t + 10/3] +   1/5 Sin[251 t + 10/3] + 2/3 Sin[252 t + 21/5] +   1/3 Sin[253 t + 1] + 3/5 Sin[254 t + 14/5] + 1/3 Sin[255 t + 35/18]y[t_] := -4/7 Sin[19/13 - 256 t] - 6/7 Sin[7/6 - 250 t] -   1/4 Sin[4/3 - 248 t] - 1/9 Sin[10/9 - 247 t] -   8/15 Sin[1/2 - 236 t] - 2/5 Sin[4/3 - 235 t] -   7/8 Sin[10/7 - 233 t] - 1/10 Sin[5/7 - 230 t] -   1/6 Sin[5/6 - 226 t] - 10/9 Sin[5/7 - 222 t] -   9/8 Sin[8/7 - 220 t] - 2/7 Sin[2/5 - 211 t] - 3/8 Sin[5/4 - 208 t] -   Sin[1/4 - 203 t] - 9/10 Sin[10/7 - 198 t] - 4/5 Sin[5/6 - 197 t] -   3/5 Sin[5/6 - 194 t] - 7/9 Sin[6/5 - 193 t] -   3/5 Sin[1/16 - 186 t] - 19/9 Sin[3/10 - 181 t] -   5/9 Sin[7/5 - 178 t] - 4/3 Sin[1/9 - 177 t] -   8/9 Sin[1/10 - 164 t] - 9/5 Sin[18/17 - 161 t] -   19/8 Sin[1/2 - 157 t] - 1/4 Sin[1/5 - 155 t] -   13/6 Sin[6/11 - 153 t] - 11/7 Sin[4/3 - 147 t] -   11/4 Sin[6/7 - 144 t] - 23/7 Sin[7/8 - 143 t] -   29/15 Sin[1/6 - 134 t] - 11/7 Sin[6/5 - 131 t] -   7/6 Sin[1 - 128 t] - 9/5 Sin[1/4 - 118 t] -   23/24 Sin[11/10 - 113 t] - 3/4 Sin[7/8 - 112 t] -   19/4 Sin[10/11 - 105 t] - 17/8 Sin[2/5 - 98 t] -   19/7 Sin[5/9 - 85 t] - 9/17 Sin[10/7 - 80 t] -   16/7 Sin[7/9 - 76 t] - 18/17 Sin[5/4 - 70 t] -   13/5 Sin[7/5 - 69 t] - 11/5 Sin[1/2 - 66 t] - 8/3 Sin[3/2 - 64 t] -   11/3 Sin[6/7 - 60 t] - 23/6 Sin[2/7 - 59 t] -   43/8 Sin[7/6 - 43 t] - 43/22 Sin[17/11 - 41 t] -   9/2 Sin[4/9 - 37 t] - 305/34 Sin[10/7 - 35 t] - 3 Sin[6/7 - 32 t] -   21/5 Sin[1/2 - 28 t] - 47/6 Sin[6/7 - 27 t] -   173/7 Sin[3/2 - 16 t] - 19/3 Sin[15/14 - 10 t] -   58/3 Sin[1 - 5 t] - 221/11 Sin[3/4 - 3 t] + 16/9 Sin[45 t] +   11/5 Sin[79 t] + 1626/5 Sin[t + 43/11] + 1462/13 Sin[2 t + 28/9] +   674/9 Sin[4 t + 20/9] + 191/7 Sin[6 t + 3/5] +   65/9 Sin[7 t + 1/18] + 224/5 Sin[8 t + 1/23] +   163/4 Sin[9 t + 1/11] + 112/3 Sin[11 t + 50/11] +   178/7 Sin[12 t + 51/13] + 118/5 Sin[13 t + 38/9] +   94/5 Sin[14 t + 18/5] + 59/4 Sin[15 t + 10/7] +   37/6 Sin[17 t + 31/9] + 299/20 Sin[18 t + 9/5] +   143/6 Sin[19 t + 30/7] + 17/5 Sin[20 t + 7/6] +   110/9 Sin[21 t + 14/5] + 31/8 Sin[22 t + 5/8] +   11 Sin[23 t + 13/3] + 139/6 Sin[24 t + 13/14] +   32/3 Sin[25 t + 4/3] + 89/6 Sin[26 t + 26/9] +   65/7 Sin[29 t + 57/14] + 113/8 Sin[30 t + 3/2] +   73/8 Sin[31 t + 17/8] + 62/9 Sin[33 t + 11/4] +   26/5 Sin[34 t + 7/3] + 20/3 Sin[36 t + 25/6] +   19/3 Sin[38 t + 11/12] + 36/7 Sin[39 t + 3/2] + 4 Sin[40 t + 7/2] +   28/5 Sin[42 t + 15/4] + 2 Sin[44 t + 18/7] +   11/6 Sin[46 t + 16/9] + 31/5 Sin[47 t + 8/5] +   51/8 Sin[48 t + 15/7] + 34/11 Sin[49 t + 7/3] +   289/48 Sin[50 t + 14/5] + 32/9 Sin[51 t + 3] +   67/11 Sin[52 t + 15/16] + 12/7 Sin[53 t + 4/3] +   43/8 Sin[54 t + 7/5] + 25/8 Sin[55 t + 23/12] +   11/10 Sin[56 t + 6/7] + 4/5 Sin[57 t + 19/5] +   26/7 Sin[58 t + 29/8] + 16/7 Sin[61 t + 21/5] +   39/11 Sin[62 t + 45/11] + 70/23 Sin[63 t + 8/5] +   8/3 Sin[65 t + 29/9] + 20/9 Sin[67 t + 6/5] +   16/5 Sin[68 t + 11/5] + 23/6 Sin[71 t + 5/7] +   7/4 Sin[72 t + 47/16] + 11/7 Sin[73 t + 13/5] +   8/5 Sin[74 t + 7/2] + 8/5 Sin[75 t + 8/7] + 17/7 Sin[77 t + 16/7] +   15/8 Sin[78 t + 13/7] + Sin[81 t + 10/7] + 29/7 Sin[82 t + 11/9] +   65/16 Sin[83 t + 14/5] + 69/17 Sin[84 t + 3/4] +   5/8 Sin[86 t + 23/5] + 34/11 Sin[87 t + 2] + 5/3 Sin[88 t + 2] +   10/3 Sin[89 t + 17/6] + 97/32 Sin[90 t + 5/3] +   53/18 Sin[91 t + 3/2] + 61/20 Sin[92 t + 19/18] +   7/8 Sin[93 t + 19/5] + 31/9 Sin[94 t + 55/18] +   19/7 Sin[95 t + 5/2] + 16/7 Sin[96 t + 19/7] + 15/4 Sin[97 t + 2] +   1/11 Sin[99 t + 1/7] + 35/12 Sin[100 t + 2/9] +   40/9 Sin[101 t + 13/3] + 33/10 Sin[102 t + 99/49] +   34/9 Sin[103 t + 7/5] + 21/11 Sin[104 t + 27/13] +   11/7 Sin[106 t + 19/5] + 10/9 Sin[107 t + 15/8] +   13/6 Sin[108 t + 17/11] + 5 Sin[109 t + 3/4] +   27/10 Sin[110 t + 17/10] + 8/9 Sin[111 t + 16/5] +   34/5 Sin[114 t + 13/7] + 41/9 Sin[115 t + 31/7] +   5/4 Sin[116 t + 67/17] + 3/4 Sin[117 t + 16/5] +   13/5 Sin[119 t + 1/4] + 14/5 Sin[120 t + 11/6] +   20/19 Sin[121 t + 3/7] + 72/13 Sin[122 t + 59/15] +   3 Sin[123 t + 1/22] + 6/7 Sin[124 t + 21/5] +   11/8 Sin[125 t + 37/8] + 23/7 Sin[126 t + 3/7] +   13/7 Sin[127 t + 29/8] + 16/15 Sin[129 t + 47/12] +   21/8 Sin[130 t + 61/15] + 19/13 Sin[132 t + 1/2] +   29/14 Sin[133 t + 10/3] + 29/8 Sin[135 t + 9/2] +   5/11 Sin[136 t + 13/8] + 71/14 Sin[137 t + 23/9] +   4/9 Sin[138 t + 13/9] + 23/10 Sin[139 t + 34/9] +   17/9 Sin[140 t + 31/8] + 21/5 Sin[141 t + 29/7] +   28/11 Sin[142 t + 7/2] + 3/5 Sin[145 t + 16/9] +   4/3 Sin[146 t + 13/6] + 6/5 Sin[148 t + 7/6] +   9/7 Sin[149 t + 28/9] + 4/3 Sin[150 t + 5/2] +   12/7 Sin[151 t + 1] + 7/4 Sin[152 t + 17/4] +   21/20 Sin[154 t + 1] + 1/4 Sin[156 t + 1/4] + 17/6 Sin[158 t + 3] +   9/4 Sin[159 t + 3/4] + 16/9 Sin[160 t + 43/21] +   4/9 Sin[162 t + 11/7] + 9/7 Sin[163 t + 46/13] +   13/7 Sin[165 t + 16/7] + 8/5 Sin[166 t + 3/10] +   11/6 Sin[167 t + 25/6] + 5/7 Sin[168 t + 39/11] +   3/4 Sin[169 t + 29/7] + 53/18 Sin[170 t + 20/21] +   24/7 Sin[171 t + 22/5] + 8/9 Sin[172 t + 11/5] +   6/13 Sin[173 t + 40/9] + 16/15 Sin[174 t + 3] +   45/22 Sin[175 t + 17/6] + 6/7 Sin[176 t + 32/7] +   9/7 Sin[179 t + 28/11] + 3/2 Sin[180 t + 29/10] +   20/19 Sin[182 t + 9/4] + 9/7 Sin[183 t + 193/48] +   11/10 Sin[184 t + 6/5] + 4/3 Sin[185 t + 18/7] +   3/5 Sin[187 t + 11/4] + 11/8 Sin[188 t + 16/11] +   3/4 Sin[189 t + 27/10] + 1/2 Sin[190 t + 1/6] +   10/7 Sin[191 t + 38/13] + 3/10 Sin[192 t + 52/15] +   4/5 Sin[195 t + 5/8] + 2/3 Sin[196 t + 5/4] +   6/5 Sin[199 t + 1/7] + 1/4 Sin[200 t + 4/5] +   5/8 Sin[201 t + 2/5] + 5/6 Sin[202 t + 87/22] +   15/14 Sin[204 t + 2/7] + 5/7 Sin[205 t + 5/7] +   2/3 Sin[206 t + 7/10] + Sin[207 t + 33/13] +   6/7 Sin[209 t + 37/8] + 3/8 Sin[210 t + 10/3] +   1/10 Sin[212 t + 6/5] + 2/5 Sin[213 t + 20/7] +   1/2 Sin[214 t + 21/8] + 17/16 Sin[215 t + 37/8] +   12/7 Sin[216 t + 19/5] + 1/5 Sin[217 t + 19/7] +   1/5 Sin[218 t + 15/4] + 1/9 Sin[219 t + 2/5] +   1/3 Sin[221 t + 5/3] + 3/4 Sin[223 t + 17/7] +   1/4 Sin[224 t + 19/13] + 1/7 Sin[225 t + 1/7] +   1/3 Sin[227 t + 16/5] + 5/7 Sin[228 t + 10/3] +   4/9 Sin[229 t + 10/7] + 9/10 Sin[231 t + 8/7] +   1/2 Sin[232 t + 13/14] + 7/10 Sin[234 t + 2] +   7/8 Sin[237 t + 9/7] + 3/5 Sin[238 t + 1/4] +   4/7 Sin[239 t + 11/5] + 1/2 Sin[240 t + 11/8] +   1/28 Sin[241 t + 5/7] + 2/7 Sin[242 t + 11/5] +   1/3 Sin[243 t + 21/5] + 1/5 Sin[244 t + 19/8] +   5/8 Sin[245 t + 18/19] + 3/4 Sin[246 t + 29/10] +   1/5 Sin[249 t + 7/10] + 5/6 Sin[251 t + 4/3] +   1/6 Sin[252 t + 22/7] + 3/4 Sin[253 t + 37/8] +   6/11 Sin[254 t + 3/2] + 5/4 Sin[255 t + 7/5] + 647/5;ParametricPlot[{x[t], y[t]}, {t, 0, 2 Pi}]