Parametric Winter Tree: Exploring Geometric Transformations

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2023-12-23 17:40

In collections Curves

This example demonstrates how to create complex geometric shapes using parametric equations. Key mathematical concepts include parametric equations, matrix operations, and geometric transformations. Construction involves using GeoGebra's CurveCartesian command and object a. Suitable for high school students learning about geometric transformations and parametric curves.

GeoGebra Commands & Parameters

CurveCartesian((-11 / 8 * sin(28 / 19 - (200 * t))) - (3 / 5 * sin(3 / 2 - (196 * t))) - (4 / 5 * sin(19 / 13 - (195 * t))) - (7 / 11 * sin(8 / 7 - (190 * t))) - (9 / 8 * sin(5 / 11 - (189 * t))) - (10 / 13 * sin(8 / 7 - (188 * t))) - (1 / 19 * sin(20 / 19 - (186 * t))) - (5 / 12 * sin(13 / 9 - (180 * t))) - (5 / 9 * sin(5 / 7 - (177 * t))) - (2 / 3 * sin(6 / 7 - (174 * t))) - (6 / 17 * sin(8 / 7 - (172 * t))) - (3 / 4 * sin(5 / 7 - (169 * t))) - (24 / 25 * sin(6 / 5 - (166 * t))) - (11 / 9 * sin(3 / 5 - (149 * t))) - (13 / 5 * sin(1 / 39 - (147 * t))) - (9 / 4 * sin(7 / 11 - (143 * t))) - (19 / 7 * sin(1 / 9 - (136 * t))) - (19 / 13 * sin(3 / 13 - (124 * t))) - (19 / 14 * sin(8 / 9 - (123 * t))) - (13 / 10 * sin(5 / 8 - (113 * t))) - (13 / 6 * sin(5 / 7 - (111 * t))) - (78 / 77 * sin(10 / 11 - (109 * t))) - (10 / 13 * sin(4 / 7 - (108 * t))) - (31 / 15 * sin(7 / 9 - (106 * t))) - (49 / 25 * sin(3 / 7 - (105 * t))) - (17 / 8 * sin(3 / 7 - (103 * t))) - (61 / 30 * sin(10 / 9 - (102 * t))) - (33 / 10 * sin(7 / 6 - (94 * t))) - (6 / 7 * sin(11 / 9 - (93 * t))) - (43 / 12 * sin(5 / 7 - (86 * t))) - (41 / 14 * sin(11 / 13 - (82 * t))) - (51 / 8 * sin(7 / 9 - (81 * t))) - (4 / 5 * sin(16 / 13 - (77 * t))) - (28 / 9 * sin(1 / 12 - (76 * t))) - (19 / 6 * sin(7 / 13 - (75 * t))) - (16 / 5 * sin(1 / 12 - (73 * t))) - (2 * sin(3 / 11 - (71 * t))) - (119 / 15 * sin(10 / 9 - (62 * t))) - (256 / 51 * sin(11 / 7 - (61 * t))) - (81 / 10 * sin(7 / 10 - (59 * t))) - (35 / 23 * sin(5 / 11 - (58 * t))) - (7 / 2 * sin(4 / 9 - (51 * t))) - (81 / 8 * sin(9 / 8 - (46 * t))) - (14 / 3 * sin(1 / 6 - (45 * t))) - (39 / 7 * sin(1 / 7 - (38 * t))) - (89 / 6 * sin(12 / 11 - (34 * t))) - (179 / 14 * sin(9 / 7 - (33 * t))) - (77 / 9 * sin(2 / 3 - (31 * t))) - (74 / 5 * sin(13 / 11 - (26 * t))) - (55 / 3 * sin(5 / 8 - (24 * t))) - (170 / 13 * sin(7 / 10 - (23 * t))) - (68 / 11 * sin(9 / 8 - (21 * t))) - (2204 / 63 * sin(18 / 19 - (17 * t))) - (352 / 15 * sin(4 / 7 - (16 * t))) - (93 / 4 * sin(8 / 7 - (15 * t))) - (403 / 10 * sin(8 / 17 - (8 * t))) - (257 / 9 * sin(5 / 6 - (7 * t))) - (5768 / 79 * sin(25 / 17 - (4 * t))) - (663 / 8 * sin(10 / 11 - (2 * t))) - (378 * sin(5 / 13 - t)) + (4 / 7 * sin((141 * t))) + (9 / 11 * sin((173 * t))) + (60 / 7 * sin((3 * t) + 28 / 9)) + (511 / 11 * sin((5 * t) + 25 / 7)) + (835 / 14 * sin((6 * t) + 93 / 23)) + (433 / 9 * sin((9 * t) + 1 / 2)) + (176 / 9 * sin((10 * t) + 37 / 10)) + (248 / 7 * sin((11 * t) + 53 / 26)) + (395 / 11 * sin((12 * t) + 7 / 5)) + (261 / 8 * sin((13 * t) + 4 / 11)) + (42 / 5 * sin((14 * t) + 55 / 27)) + (29 / 2 * sin((18 * t) + 37 / 12)) + (43 / 9 * sin((19 * t) + 1 / 14)) + (21 / 10 * sin((20 * t) + 21 / 8)) + (45 / 4 * sin((22 * t) + 1 / 11)) + (24 / 7 * sin((25 * t) + 24 / 7)) + (115 / 21 * sin((27 * t) + 51 / 11)) + (22 / 5 * sin((28 * t) + 68 / 15)) + (44 / 5 * sin((29 * t) + 11 / 3)) + (25 / 8 * sin((30 * t) + 4 / 3)) + (133 / 8 * sin((32 * t) + 14 / 3)) + (11 / 12 * sin((35 * t) + 54 / 13)) + (79 / 8 * sin((36 * t) + 5 / 3)) + (47 / 6 * sin((37 * t) + 3 / 2)) + (75 / 8 * sin((39 * t) + 33 / 14)) + (22 / 5 * sin((40 * t) + 5 / 7)) + (85 / 19 * sin((41 * t) + 23 / 5)) + (223 / 32 * sin((42 * t) + 17 / 4)) + (49 / 8 * sin((43 * t) + 4)) + (79 / 8 * sin((44 * t) + 2)) + (51 / 10 * sin((47 * t) + 4 / 7)) + (41 / 6 * sin((48 * t) + 17 / 11)) + (140 / 11 * sin((49 * t) + 17 / 8)) + (5 * sin((50 * t) + 20 / 19)) + (13 / 5 * sin((52 * t) + 13 / 6)) + (47 / 12 * sin((53 * t) + 50 / 11)) + (75 / 13 * sin((54 * t) + 11 / 7)) + (17 / 8 * sin((55 * t) + 1 / 8)) + (93 / 14 * sin((56 * t) + 29 / 10)) + (41 / 8 * sin((57 * t) + 1 / 17)) + (7 / 2 * sin((60 * t) + 32 / 31)) + (47 / 12 * sin((63 * t) + 46 / 11)) + (97 / 16 * sin((64 * t) + 48 / 13)) + (13 / 7 * sin((65 * t) + 65 / 14)) + (33 / 8 * sin((66 * t) + 43 / 12)) + (11 / 2 * sin((67 * t) + 17 / 8)) + (54 / 11 * sin((68 * t) + 19 / 6)) + (53 / 16 * sin((69 * t) + 25 / 9)) + (39 / 5 * sin((70 * t) + 23 / 13)) + (37 / 13 * sin((72 * t) + 21 / 11)) + (24 / 7 * sin((74 * t) + 77 / 17)) + (25 / 4 * sin((78 * t) + 17 / 10)) + (17 / 7 * sin((79 * t) + 53 / 21)) + (13 / 9 * sin((80 * t) + 5 / 7)) + (30 / 11 * sin((83 * t) + 8 / 11)) + (31 / 13 * sin((84 * t) + 9 / 8)) + (28 / 9 * sin((85 * t) + 28 / 9)) + (57 / 56 * sin((87 * t) + 12 / 7)) + (20 / 11 * sin((88 * t) + 34 / 9)) + (15 / 4 * sin((89 * t) + 35 / 11)) + (10 / 3 * sin((90 * t) + 19 / 18)) + (46 / 11 * sin((91 * t) + 23 / 10)) + (61 / 20 * sin((92 * t) + 1 / 3)) + (14 / 5 * sin((95 * t) + 24 / 11)) + (30 / 7 * sin((96 * t) + 7 / 13)) + (3 / 2 * sin((97 * t) + 21 / 5)) + (10 / 9 * sin((98 * t) + 59 / 20)) + (57 / 17 * sin((99 * t) + 10 / 7)) + (7 / 4 * sin((100 * t) + 59 / 16)) + (7 / 2 * sin((101 * t) + 20 / 7)) + (42 / 13 * sin((104 * t) + 13 / 11)) + (31 / 16 * sin((107 * t) + 31 / 11)) + (43 / 12 * sin((110 * t) + 3 / 7)) + (24 / 13 * sin((112 * t) + 29 / 11)) + (11 / 6 * sin((114 * t) + 4 / 13)) + (24 / 7 * sin((115 * t) + 22 / 9)) + (6 / 7 * sin((116 * t) + 29 / 9)) + (12 / 11 * sin((117 * t) + 5 / 3)) + (98 / 33 * sin((118 * t) + 13 / 5)) + (17 / 9 * sin((119 * t) + 20 / 9)) + (24 / 23 * sin((120 * t) + 5 / 4)) + (9 / 8 * sin((121 * t) + 43 / 12)) + (38 / 15 * sin((122 * t) + 17 / 7)) + (3 / 7 * sin((125 * t) + 3 / 8)) + (7 / 6 * sin((126 * t) + 19 / 5)) + (3 / 4 * sin((127 * t) + 7 / 10)) + (19 / 10 * sin((128 * t) + 33 / 8)) + (7 / 6 * sin((129 * t) + 11 / 4)) + (17 / 12 * sin((130 * t) + 29 / 7)) + (3 / 2 * sin((131 * t) + 3 / 2)) + (5 / 14 * sin((132 * t) + 7 / 12)) + (36 / 11 * sin((133 * t) + 87 / 25)) + (17 / 14 * sin((134 * t) + 37 / 10)) + (16 / 13 * sin((135 * t) + 31 / 15)) + (9 / 8 * sin((137 * t) + 19 / 8)) + (25 / 24 * sin((138 * t) + 18 / 13)) + (2 / 7 * sin((139 * t) + 12 / 7)) + (1 / 4 * sin((140 * t) + 29 / 12)) + (7 / 5 * sin((142 * t) + 43 / 12)) + (32 / 31 * sin((144 * t) + 3 / 7)) + (20 / 19 * sin((145 * t) + 23 / 10)) + (9 / 7 * sin((146 * t) + 26 / 11)) + (19 / 14 * sin((148 * t) + 47 / 16)) + (7 / 13 * sin((150 * t) + 50 / 11)) + (5 / 4 * sin((151 * t) + 22 / 15)) + (14 / 9 * sin((152 * t) + 29 / 12)) + (5 / 9 * sin((153 * t) + 19 / 5)) + (24 / 23 * sin((154 * t) + 19 / 9)) + (8 / 9 * sin((155 * t) + 13 / 3)) + (23 / 9 * sin((156 * t) + 23 / 8)) + sin((157 * t) + 57 / 17) + (37 / 36 * sin((158 * t) + 1 / 3)) + (4 / 5 * sin((159 * t) + 19 / 15)) + (7 / 15 * sin((160 * t) + 25 / 8)) + (3 / 10 * sin((161 * t) + 5 / 11)) + (3 / 7 * sin((162 * t) + 29 / 14)) + (18 / 11 * sin((163 * t) + 14 / 3)) + (5 / 7 * sin((164 * t) + 19 / 7)) + (19 / 13 * sin((165 * t) + 36 / 11)) + (3 / 4 * sin((167 * t) + 1 / 8)) + (5 / 9 * sin((168 * t) + 45 / 11)) + (21 / 22 * sin((170 * t) + 28 / 9)) + (17 / 14 * sin((171 * t) + 13 / 7)) + (1 / 10 * sin((175 * t) + 25 / 7)) + (10 / 21 * sin((176 * t) + 7 / 2)) + (11 / 9 * sin((178 * t) + 34 / 9)) + (4 / 9 * sin((179 * t) + 20 / 19)) + (8 / 7 * sin((181 * t) + 74 / 17)) + (5 / 7 * sin((182 * t) + 171 / 43)) + (9 / 8 * sin((183 * t) + 13 / 8)) + (6 / 19 * sin((184 * t) + 2 / 5)) + (11 / 10 * sin((185 * t) + 37 / 11)) + (1 / 4 * sin((187 * t) + 31 / 9)) + (4 / 15 * sin((191 * t) + 2 / 9)) + (5 / 9 * sin((192 * t) + 134 / 45)) + (3 / 8 * sin((193 * t) + 26 / 7)) + (9 / 19 * sin((194 * t) + 20 / 7)) + (5 / 8 * sin((197 * t) + 4 / 9)) + (4 / 11 * sin((198 * t) + 11 / 3)) + (19 / 20 * sin((199 * t) + 3 / 7)) + (7 / 11 * sin((201 * t) + 7 / 8)) + 145 / 11, (-1 / 15 * sin(2 / 3 - (196 * t))) - (3 / 8 * sin(15 / 11 - (193 * t))) - (3 / 5 * sin(35 / 34 - (191 * t))) - (5 / 8 * sin(15 / 14 - (178 * t))) - (1 / 4 * sin(1 / 4 - (175 * t))) - (5 / 9 * sin(10 / 7 - (174 * t))) - (44 / 43 * sin(4 / 13 - (172 * t))) - (6 / 7 * sin(9 / 8 - (171 * t))) - (27 / 28 * sin(2 / 9 - (165 * t))) - (7 / 9 * sin(4 / 7 - (160 * t))) - (13 / 11 * sin(3 / 11 - (158 * t))) - (21 / 13 * sin(11 / 12 - (157 * t))) - (46 / 31 * sin(8 / 7 - (155 * t))) - (9 / 5 * sin(3 / 4 - (149 * t))) - (8 / 15 * sin(4 / 5 - (148 * t))) - (10 / 9 * sin(8 / 7 - (145 * t))) - (34 / 33 * sin(7 / 5 - (144 * t))) - (6 / 7 * sin(23 / 15 - (138 * t))) - sin(9 / 13 - (134 * t)) - (27 / 10 * sin(18 / 17 - (133 * t))) - (13 / 12 * sin(43 / 42 - (129 * t))) - (9 / 5 * sin(1 / 11 - (128 * t))) - (7 / 6 * sin(4 / 3 - (125 * t))) - (8 / 9 * sin(1 / 2 - (123 * t))) - (41 / 15 * sin(19 / 20 - (122 * t))) - (3 / 5 * sin(8 / 13 - (121 * t))) - (23 / 10 * sin(2 / 13 - (120 * t))) - (34 / 23 * sin(1 / 3 - (111 * t))) - (17 / 8 * sin(28 / 27 - (107 * t))) - (23 / 12 * sin(6 / 7 - (103 * t))) - (9 / 4 * sin(6 / 7 - (101 * t))) - (57 / 28 * sin(2 / 7 - (100 * t))) - (13 / 8 * sin(2 / 5 - (97 * t))) - (39 / 19 * sin(11 / 13 - (94 * t))) - (20 / 9 * sin(7 / 6 - (89 * t))) - (3 / 7 * sin(5 / 4 - (88 * t))) - (17 / 9 * sin(5 / 6 - (82 * t))) - (8 / 3 * sin(4 / 9 - (77 * t))) - (33 / 7 * sin(1 / 18 - (66 * t))) - (16 / 7 * sin(4 / 7 - (64 * t))) - (43 / 7 * sin(16 / 13 - (63 * t))) - (31 / 7 * sin(19 / 13 - (57 * t))) - (60 / 13 * sin(1 / 17 - (56 * t))) - (61 / 10 * sin(11 / 7 - (45 * t))) - (111 / 10 * sin(7 / 15 - (43 * t))) - (164 / 15 * sin(17 / 11 - (40 * t))) - (46 / 11 * sin(32 / 31 - (35 * t))) - (43 / 4 * sin(37 / 36 - (31 * t))) - (32 / 11 * sin(13 / 9 - (28 * t))) - (57 / 4 * sin(1 / 18 - (24 * t))) - (51 / 5 * sin(9 / 11 - (18 * t))) - (54 / 5 * sin(5 / 4 - (15 * t))) - (183 / 8 * sin(1 / 93 - (14 * t))) - (78 / 7 * sin(7 / 11 - (10 * t))) + (4879 / 12 * sin(t + 31 / 7)) + (925 / 6 * sin((2 * t) + 51 / 14)) + (469 / 15 * sin((3 * t) + 32 / 7)) + (1285 / 11 * sin((4 * t) + 41 / 15)) + (89 / 3 * sin((5 * t) + 27 / 8)) + (411 / 5 * sin((6 * t) + 22 / 13)) + (317 / 8 * sin((7 * t) + 24 / 11)) + (169 / 10 * sin((8 * t) + 9 / 4)) + (87 / 10 * sin((9 * t) + 22 / 5)) + (193 / 8 * sin((11 * t) + 25 / 9)) + (242 / 23 * sin((12 * t) + 23 / 5)) + (181 / 7 * sin((13 * t) + 22 / 7)) + (76 / 7 * sin((16 * t) + 15 / 16)) + (159 / 7 * sin((17 * t) + 9 / 7)) + (108 / 5 * sin((19 * t) + 1 / 41)) + (287 / 25 * sin((20 * t) + 33 / 13)) + (32 / 3 * sin((21 * t) + 40 / 11)) + (243 / 10 * sin((22 * t) + 11 / 10)) + (65 / 6 * sin((23 * t) + 41 / 13)) + (39 / 14 * sin((25 * t) + 6 / 17)) + (103 / 10 * sin((26 * t) + 17 / 12)) + (23 / 4 * sin((27 * t) + 14 / 9)) + (34 / 5 * sin((29 * t) + 55 / 13)) + (43 / 7 * sin((30 * t) + 65 / 22)) + (161 / 12 * sin((32 * t) + 11 / 9)) + (21 / 16 * sin((33 * t) + 7 / 5)) + (42 / 11 * sin((34 * t) + 28 / 11)) + (26 / 3 * sin((36 * t) + 33 / 10)) + (79 / 11 * sin((37 * t) + 48 / 13)) + (118 / 39 * sin((38 * t) + 19 / 11)) + (106 / 13 * sin((39 * t) + 47 / 12)) + (79 / 16 * sin((41 * t) + 23 / 24)) + (37 / 9 * sin((42 * t) + 97 / 32)) + (83 / 8 * sin((44 * t) + 74 / 21)) + (72 / 11 * sin((46 * t) + 10 / 19)) + (43 / 8 * sin((47 * t) + 86 / 29)) + (17 / 12 * sin((48 * t) + 43 / 10)) + (43 / 4 * sin((49 * t) + 25 / 6)) + (52 / 9 * sin((50 * t) + 2 / 5)) + (233 / 29 * sin((51 * t) + 37 / 19)) + (16 / 11 * sin((52 * t) + 11 / 4)) + (68 / 11 * sin((53 * t) + 43 / 10)) + (81 / 7 * sin((54 * t) + 37 / 11)) + (21 / 11 * sin((55 * t) + 1 / 3)) + (29 / 14 * sin((58 * t) + 25 / 6)) + (43 / 10 * sin((59 * t) + 5 / 8)) + (19 / 7 * sin((60 * t) + 13 / 3)) + (29 / 15 * sin((61 * t) + 3)) + (6 / 7 * sin((62 * t) + 37 / 11)) + (5 * sin((65 * t) + 31 / 12)) + (6 / 5 * sin((67 * t) + 8 / 7)) + (42 / 11 * sin((68 * t) + 1 / 12)) + (47 / 10 * sin((69 * t) + 12 / 7)) + (50 / 17 * sin((70 * t) + 25 / 7)) + (19 / 9 * sin((71 * t) + 17 / 7)) + (17 / 7 * sin((72 * t) + 25 / 13)) + (37 / 16 * sin((73 * t) + 5 / 2)) + (17 / 13 * sin((74 * t) + 7 / 6)) + (89 / 15 * sin((75 * t) + 9 / 13)) + (22 / 13 * sin((76 * t) + 27 / 7)) + (21 / 10 * sin((78 * t) + 8 / 3)) + (21 / 5 * sin((79 * t) + 3 / 7)) + (37 / 8 * sin((80 * t) + 63 / 16)) + (71 / 13 * sin((81 * t) + 7 / 10)) + (133 / 33 * sin((83 * t) + 13 / 5)) + (23 / 7 * sin((84 * t) + 17 / 12)) + (10 / 9 * sin((85 * t) + 10 / 3)) + (61 / 14 * sin((86 * t) + 27 / 16)) + (25 / 6 * sin((87 * t) + 17 / 5)) + (35 / 8 * sin((90 * t) + 16 / 7)) + (29 / 19 * sin((91 * t) + 41 / 9)) + (14 / 11 * sin((92 * t) + 11 / 9)) + (25 / 14 * sin((93 * t) + 25 / 7)) + (19 / 8 * sin((95 * t) + 26 / 7)) + (48 / 11 * sin((96 * t) + 16 / 7)) + (49 / 25 * sin((98 * t) + 23 / 8)) + (9 / 4 * sin((99 * t) + 40 / 11)) + (9 / 5 * sin((102 * t) + 17 / 11)) + (15 / 7 * sin((104 * t) + 9 / 4)) + (10 / 9 * sin((105 * t) + 8 / 5)) + (35 / 8 * sin((106 * t) + 4 / 9)) + (1 / 4 * sin((108 * t) + 25 / 11)) + (17 / 13 * sin((109 * t) + 13 / 8)) + (39 / 8 * sin((110 * t) + 37 / 14)) + (25 / 7 * sin((112 * t) + 11 / 3)) + (148 / 49 * sin((113 * t) + 1 / 2)) + (2 * sin((114 * t) + 1)) + (56 / 15 * sin((115 * t) + 27 / 8)) + (5 / 9 * sin((116 * t) + 5 / 7)) + (11 / 6 * sin((117 * t) + 31 / 7)) + (21 / 10 * sin((118 * t) + 24 / 7)) + (14 / 9 * sin((119 * t) + 29 / 8)) + (9 / 5 * sin((124 * t) + 2)) + (6 / 5 * sin((126 * t) + 15 / 7)) + (13 / 25 * sin((127 * t) + 26 / 17)) + sin((130 * t) + 13 / 6) + (23 / 14 * sin((131 * t) + 17 / 7)) + (13 / 10 * sin((132 * t) + 11 / 5)) + (1 / 4 * sin((135 * t) + 62 / 17)) + (32 / 11 * sin((136 * t) + 15 / 7)) + (5 / 6 * sin((137 * t) + 37 / 10)) + (6 / 7 * sin((139 * t) + 9 / 2)) + (11 / 23 * sin((140 * t) + 13 / 8)) + (5 / 3 * sin((141 * t) + 41 / 11)) + (11 / 7 * sin((142 * t) + 46 / 11)) + (11 / 8 * sin((143 * t) + 1 / 2)) + (4 / 3 * sin((146 * t) + 2)) + (3 / 8 * sin((147 * t) + 38 / 13)) + (7 / 6 * sin((150 * t) + 13 / 8)) + (11 / 9 * sin((151 * t) + 25 / 6)) + (29 / 28 * sin((152 * t) + 4 / 9)) + (7 / 11 * sin((153 * t) + 14 / 11)) + (28 / 17 * sin((154 * t) + 20 / 11)) + (4 / 5 * sin((156 * t) + 26 / 15)) + (14 / 9 * sin((159 * t) + 4 / 3)) + (7 / 9 * sin((161 * t) + 51 / 25)) + (1 / 14 * sin((162 * t) + 1 / 3)) + (6 / 7 * sin((163 * t) + 85 / 21)) + (14 / 11 * sin((164 * t) + 16 / 9)) + (9 / 11 * sin((166 * t) + 25 / 8)) + (8 / 13 * sin((167 * t) + 9 / 13)) + (16 / 13 * sin((168 * t) + 24 / 7)) + (11 / 15 * sin((169 * t) + 13 / 7)) + (26 / 25 * sin((170 * t) + 68 / 15)) + (4 / 3 * sin((173 * t) + 59 / 20)) + (6 / 13 * sin((176 * t) + 8 / 9)) + (3 / 4 * sin((177 * t) + 2 / 9)) + (1 / 3 * sin((179 * t) + 17 / 6)) + (1 / 2 * sin((180 * t) + 11 / 3)) + (7 / 11 * sin((181 * t) + 4 / 15)) + (2 * sin((182 * t) + 18 / 13)) + (8 / 11 * sin((183 * t) + 23 / 6)) + (4 / 9 * sin((184 * t) + 2)) + (7 / 8 * sin((185 * t) + 33 / 10)) + (7 / 11 * sin((186 * t) + 7 / 15)) + (5 / 4 * sin((187 * t) + 31 / 13)) + (8 / 15 * sin((188 * t) + 70 / 19)) + (11 / 15 * sin((189 * t) + 74 / 21)) + (5 / 14 * sin((190 * t) + 25 / 7)) + (3 / 7 * sin((192 * t) + 12 / 23)) + (3 / 7 * sin((194 * t) + 8 / 11)) + (2 / 9 * sin((195 * t) + 43 / 12)) + (13 / 10 * sin((197 * t) + 3 / 5)) + (5 / 9 * sin((198 * t) + 23 / 6)) + (3 / 7 * sin((199 * t) + 9 / 5)) + (5 / 7 * sin((200 * t) + 3)) + (3 / 5 * sin((201 * t) + 9 / 8)) + 1910 / 9, t, 0, (2 * pi)) → a

AI Drawing Prompt Reference

Draw a winter tree formed by a complex parametric curve, with a trunk rising from the bottom and branching into a dense, irregular canopy. The outline is built from many superimposed sine waves, creating jagged, natural-looking branches and twigs. Use a monochrome or dark line style, with the tree filling the frame. The overall shape should evoke a bare winter tree, with intricate, fractal-like details resulting from the mathematical superposition of frequencies.

The prompt above was compiled from the original drawing commands and is for reference only.