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Pythagora’s Tree Fractal via Iterated Semicircles

Pythagora’s Tree Fractal via Iterated Semicircles
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2021-01-28 23:45
CirclePolygonAngleTransformationGeometric Construction
This GeoGebra example demonstrates the classic Pythagora’s Tree fractal by repeatedly constructing semicircles on the sides of right triangles and iterating the pattern through controlled rotations. It visually highlights how a self-similar structure grows step by step from an initial configuration. The key math ideas include fractal geometry (self-similarity), right-triangle construction inspired by the Pythagorean relationship, and precise circular/semicircular geometry. Construction-wise, it uses GeoGebra commands such as Segment, Semicircle, Circle, Midpoint, Rotate, and Angle, together with a CustomSquare tool to create the initial right-angle framework. Subsequent iterations rely on rotating derived points and assembling shapes (points like A, B, D, E, A′, F, G, H and polygon collections such as poly1/poly2/poly3) to build the multi-level fractal outline. Suitable for middle/high school enrichment, competition-style geometry, and classroom demonstrations of fractals and geometric construction.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Semicircle(A, B) → c
  3. CustomSquare(B, A) → D, E, d, e, f, g, poly2
  4. Midpoint(d) → J
  5. Circle(J, A) → q
  6. Rotate(A, (-α), J) → A'
  7. CustomSquare(A, A') → C, F, b, h, i, j, poly1
  8. CustomSquare(A', B) → G, H, k, l, m, n, poly3
  9. Midpoint(i) → I
  10. Midpoint(m) → K
  11. Circle(I, C) → p
  12. Circle(K, H) → r
  13. Rotate(F, (-α), I) → F'
  14. Angle(F', I, F) → β
  15. Rotate(H, (-α), K) → H'
  16. Angle(H', K, H) → γ
  17. CustomSquare(F, F') → L, M, s, t_{58}, a_1, b_1, poly4
  18. CustomSquare(F', C) → N, O, c_1, d_1, e_1, f_1, poly5
  19. CustomSquare(H, H') → P, Q, g_1, h_1, i_1, j_1, poly6
  20. CustomSquare(H', G) → R, S, k_1, l_1, m_1, n_1, poly7
  21. Midpoint(e_1) → T
  22. Midpoint(a_1) → U
  23. Midpoint(i_1) → V
  24. Circle(T, O) → p_1
  25. Circle(U, M) → q_1
  26. Circle(V, P) → r_1
  27. Midpoint(m_1) → W
  28. Circle(W, R) → s_1
  29. Rotate(M, (-α), U) → M'
  30. Angle(M', U, M) → δ
  31. Rotate(O, (-α), T) → O'
  32. Rotate(Q, (-α), V) → Q'
  33. Rotate(S, (-α), W) → S'
  34. CustomSquare(M, M') → Z, A_1, t_1, a_2, b_2, c_2, poly8
  35. CustomSquare(M', L) → B_1, C_1, d_2, e_2, f_2, g_2, poly9
  36. CustomSquare(O, O') → D_1, E_1, h_2, i_2, j_2, k_2, poly10
  37. CustomSquare(O', N) → F_1, G_1, l_2, m_2, n_2, p_2, poly11
  38. CustomSquare(Q, Q') → H_1, I_1, q_2, r_2, s_2, t_2, poly12
  39. CustomSquare(Q', P) → J_1, K_1, a_3, b_3, c_3, d_3, poly13
  40. CustomSquare(S, S') → L_1, M_1, e_3, f_3, g_3, h_3, poly14
  41. CustomSquare(S', R) → N_1, O_1, i_3, j_3, k_3, l_3, poly15
  42. Midpoint(b_2) → P_1
  43. Midpoint(f_2) → Q_1
  44. Midpoint(j_2) → R_1
  45. Midpoint(n_2) → S_1
  46. Midpoint(s_2) → T_1
  47. Midpoint(c_3) → U_1
  48. Midpoint(g_3) → V_1
  49. Midpoint(k_3) → W_1
  50. Circle(P_1, A_1) → p_3
  51. Circle(Q_1, C_1) → q_3
  52. Circle(R_1, E_1) → r_3
  53. Circle(S_1, G_1) → s_3
  54. Circle(T_1, I_1) → t_3
  55. Circle(U_1, K_1) → c_4
  56. Circle(V_1, M_1) → d_4
  57. Circle(W_1, O_1) → e_4
  58. Rotate(A_1, (-α), P_1) → Z_1
  59. Rotate(C_1, (-α), Q_1) → A_2
  60. Rotate(E_1, α, R_1) → B_2
  61. Rotate(E_1, (-α), R_1) → C_2
  62. Rotate(G_1, (-α), S_1) → D_2
  63. Rotate(I_1, (-α), T_1) → E_2
  64. Rotate(K_1, (-α), U_1) → F_2
  65. Rotate(M_1, (-α), V_1) → G_2
  66. Rotate(O_1, (-α), W_1) → H_2
  67. CustomSquare(A_1, Z_1) → I_2, J_2, m_3, n_3, a_4, b_4, poly16
  68. CustomSquare(Z_1, Z) → K_2, L_2, f_4, g_4, h_4, i_4, poly17
  69. CustomSquare(C_1, A_2) → M_2, N_2, j_4, k_4, l_4, m_4, poly18
  70. CustomSquare(A_2, B_1) → O_2, P_2, n_4, p_4, q_4, r_4, poly19
  71. CustomSquare(E_1, C_2) → Q_2, R_2, s_4, t_4, a_5, b_5, poly20
  72. CustomSquare(C_2, D_1) → S_2, T_2, c_5, d_5, e_5, f_5, poly21
  73. CustomSquare(G_1, D_2) → U_2, V_2, g_5, h_5, i_5, j_5, poly22
  74. CustomSquare(D_2, F_1) → W_2, Z_2, k_5, l_5, m_5, n_5, poly23
  75. CustomSquare(I_1, E_2) → A_3, B_3, p_5, q_5, r_5, s_5, poly24
  76. CustomSquare(E_2, H_1) → C_3, D_3, t_5, a_6, b_6, c_6, poly25
  77. CustomSquare(K_1, F_2) → E_3, F_3, d_6, e_6, f_6, g_6, poly26
  78. CustomSquare(F_2, J_1) → G_3, H_3, h_6, i_6, j_6, k_6, poly27
  79. CustomSquare(M_1, G_2) → I_3, J_3, l_6, m_6, n_6, p_6, poly28
  80. CustomSquare(G_2, L_1) → K_3, L_3, q_6, r_6, s_6, t_6, poly29
  81. CustomSquare(O_1, H_2) → M_3, N_3, a_7, b_7, c_7, d_7, poly30
  82. CustomSquare(H_2, N_1) → O_3, P_3, e_7, f_7, g_7, h_7, poly31
  83. Midpoint(a_4) → Q_3
  84. Midpoint(h_4) → R_3
  85. Midpoint(l_4) → S_3
  86. Midpoint(q_4) → T_3
  87. Midpoint(q_4) → U_3
  88. Circle(Q_3, J_2) → k_7
  89. Circle(R_3, L_2) → p_7
  90. Circle(S_3, N_2) → q_7
  91. Circle(U_3, O_2) → r_7
  92. Rotate(J_2, (-α), Q_3) → V_3
  93. Rotate(L_2, (-α), R_3) → W_3
  94. Rotate(N_2, (-α), S_3) → Z_3
  95. Rotate(P_2, (-α), U_3) → A_4
  96. CustomSquare(J_2, V_3) → B_4, C_4, i_7, j_7, l_7, m_7, poly32
  97. CustomSquare(V_3, I_2) → D_4, E_4, n_7, s_7, t_7, a_8, poly33
  98. CustomSquare(L_2, W_3) → F_4, G_4, b_8, c_8, d_8, e_8, poly34
  99. CustomSquare(W_3, K_2) → H_4, I_4, f_8, g_8, h_8, i_8, poly35
  100. CustomSquare(N_2, Z_3) → J_4, K_4, j_8, k_8, l_8, m_8, poly36
  101. CustomSquare(Z_3, M_2) → L_4, M_4, n_8, p_8, q_8, r_8, poly37
  102. CustomSquare(P_2, A_4) → N_4, O_4, s_8, t_8, a_9, b_9, poly38
  103. CustomSquare(A_4, O_2) → P_4, Q_4, c_9, d_9, e_9, f_9, poly39
  104. Midpoint(a_5) → R_4
  105. Midpoint(i_5) → S_4
  106. Midpoint(m_5) → T_4
  107. Midpoint(r_5) → U_4
  108. Midpoint(b_6) → V_4
  109. Midpoint(f_6) → W_4
  110. Midpoint(j_6) → Z_4
  111. Midpoint(n_6) → A_5
  112. Midpoint(s_6) → B_5
  113. Midpoint(c_7) → C_5
  114. Midpoint(g_7) → D_5
  115. Circle(D_5, P_3) → g_9
  116. Circle(C_5, N_3) → h_9
  117. Circle(B_5, L_3) → k_9
  118. Circle(A_5, J_3) → p_9
  119. Rotate(J_3, (-α), A_5) → E_5
  120. Rotate(L_3, (-α), B_5) → F_5
  121. Rotate(P_3, (-α), D_5) → H_5
  122. Rotate(N_3, (-α), C_5) → G_5
  123. CustomSquare(J_3, E_5) → I_5, J_5, i_9, j_9, l_9, m_9, poly40
  124. CustomSquare(E_5, I_3) → K_5, L_5, n_9, q_9, r_9, s_9, poly41
  125. CustomSquare(L_3, F_5) → M_5, N_5, t_9, a_{10}, b_{10}, c_{10}, poly42
  126. CustomSquare(F_5, K_3) → O_5, P_5, d_{10}, e_{10}, f_{10}, g_{10}, poly43
  127. CustomSquare(N_3, G_5) → Q_5, R_5, h_{10}, i_{10}, j_{10}, k_{10}, poly44
  128. CustomSquare(G_5, M_3) → S_5, T_5, l_{10}, m_{10}, n_{10}, p_{10}, poly45
  129. CustomSquare(P_3, H_5) → U_5, V_5, q_{10}, r_{10}, s_{10}, t_{10}, poly46
  130. CustomSquare(H_5, O_3) → W_5, Z_5, a_{11}, b_{11}, c_{11}, d_{11}, poly47
  131. Circle(R_4, R_2) → e_{11}
  132. Circle(S_4, V_2) → f_{11}
  133. Circle(T_4, Z_2) → g_{11}
  134. Circle(U_4, B_3) → h_{11}
  135. Circle(V_4, D_3) → k_{11}
  136. Circle(W_4, F_3) → p_{11}
  137. Circle(Z_4, H_3) → q_{11}
  138. Midpoint(e_5) → A_6
  139. Circle(A_6, T_2) → r_{11}
  140. Rotate(R_2, (-α), R_4) → B_6
  141. Rotate(T_2, (-α), A_6) → C_6
  142. Rotate(V_2, (-α), S_4) → D_6
  143. Rotate(Z_2, (-α), T_4) → F_6
  144. Rotate(B_3, (-α), U_4) → G_6
  145. Rotate(D_3, (-α), V_4) → H_6
  146. Rotate(F_3, (-α), W_4) → I_6
  147. Rotate(H_3, (-α), Z_4) → J_6
  148. CustomSquare(R_2, B_6) → K_6, L_6, i_{11}, j_{11}, l_{11}, m_{11}, poly48
  149. CustomSquare(B_6, Q_2) → M_6, N_6, n_{11}, s_{11}, t_{11}, a_{12}, poly49
  150. CustomSquare(T_2, C_6) → O_6, P_6, b_{12}, c_{12}, d_{12}, e_{12}, poly50
  151. CustomSquare(C_6, S_2) → Q_6, R_6, f_{12}, g_{12}, h_{12}, i_{12}, poly51
  152. CustomSquare(V_2, D_6) → S_6, T_6, j_{12}, k_{12}, l_{12}, m_{12}, poly52
  153. CustomSquare(D_6, U_2) → U_6, V_6, n_{12}, p_{12}, q_{12}, r_{12}, poly53
  154. CustomSquare(Z_2, F_6) → W_6, Z_6, s_{12}, t_{12}, a_{13}, b_{13}, poly54
  155. CustomSquare(B_3, G_6) → C_7, D_7, g_{13}, h_{13}, i_{13}, j_{13}, poly56
  156. CustomSquare(G_6, A_3) → E_6, E_7, k_{13}, l_{13}, m_{13}, n_{13}, poly57
  157. CustomSquare(D_3, H_6) → F_7, G_7, p_{13}, q_{13}, r_{13}, s_{13}, poly58
  158. CustomSquare(H_6, C_3) → H_7, I_7, t_{13}, a_{14}, b_{14}, c_{14}, poly59
  159. CustomSquare(F_3, I_6) → J_7, K_7, d_{14}, e_{14}, f_{14}, g_{14}, poly60
  160. CustomSquare(I_6, E_3) → L_7, M_7, h_{14}, i_{14}, j_{14}, k_{14}, poly61
  161. CustomSquare(H_3, J_6) → N_7, O_7, l_{14}, m_{14}, n_{14}, p_{14}, poly62
  162. CustomSquare(J_6, G_3) → P_7, Q_7, q_{14}, r_{14}, s_{14}, t_{14}, poly63
  163. CustomSquare(F_6, W_2) → A_7, B_7, c_{13}, d_{13}, e_{13}, f_{13}, poly55
  164. Midpoint(l_7) → R_7
  165. Midpoint(t_7) → S_7
  166. Midpoint(d_8) → T_7
  167. Midpoint(h_8) → U_7
  168. Midpoint(l_8) → V_7
  169. Midpoint(q_8) → W_7
  170. Midpoint(a_9) → Z_7
  171. Midpoint(e_9) → A_8
  172. Midpoint(l_{11}) → B_8
  173. Midpoint(t_{11}) → C_8
  174. Midpoint(h_{12}) → E_8
  175. Midpoint(l_{12}) → F_8
  176. Midpoint(q_{12}) → G_8
  177. Midpoint(a_{13}) → H_8
  178. Midpoint(i_{13}) → I_8
  179. Midpoint(m_{13}) → J_8
  180. Midpoint(e_{13}) → K_8
  181. Midpoint(f_{14}) → L_8
  182. Midpoint(j_{14}) → M_8
  183. Midpoint(n_{14}) → N_8
  184. Midpoint(s_{14}) → O_8
  185. Midpoint(r_9) → P_8
  186. Midpoint(l_9) → Q_8
  187. Midpoint(b_{10}) → R_8
  188. Midpoint(f_{10}) → S_8
  189. Midpoint(j_{10}) → T_8
  190. Midpoint(n_{10}) → U_8
  191. Midpoint(s_{10}) → V_8
  192. Midpoint(d_{11}) → W_8
  193. Midpoint(c_{11}) → Z_8
  194. Midpoint(r_{13}) → A_9
  195. Midpoint(b_{14}) → B_9
  196. Circle(Z_8, Z_5) → c_{15}
  197. Circle(V_8, U_5) → d_{15}
  198. Circle(U_8, T_5) → e_{15}
  199. Circle(T_8, R_5) → f_{15}
  200. Circle(S_8, P_5) → g_{15}
  201. Circle(R_8, N_5) → h_{15}
  202. Circle(P_8, L_5) → k_{15}
  203. Circle(N_8, O_7) → p_{15}
  204. Circle(M_8, M_7) → q_{15}
  205. Circle(B_9, I_7) → r_{15}
  206. Circle(A_9, F_7) → s_{15}
  207. Circle(G_8, V_6) → t_{15}
  208. Circle(F_8, S_6) → c_{16}
  209. Circle(E_8, R_6) → d_{16}
  210. Circle(C_8, M_6) → f_{16}
  211. Circle(Z_7, N_4) → g_{16}
  212. Circle(W_7, L_4) → h_{16}
  213. Circle(V_7, J_4) → k_{16}
  214. Circle(U_7, H_4) → p_{16}
  215. Circle(T_7, F_4) → q_{16}
  216. Circle(S_7, D_4) → r_{16}
  217. Circle(R_7, C_4) → s_{16}
  218. Circle(K_8, B_7) → t_{16}
  219. Circle(H_8, W_6) → c_{17}
  220. Circle(A_8, P_4) → d_{17}
  221. Circle(O_8, Q_7) → e_{17}
  222. Rotate(Z_5, (-α), Z_8) → C_9
  223. Rotate(V_5, (-α), V_8) → D_9
  224. Rotate(T_5, (-α), U_8) → E_9
  225. Rotate(R_5, (-α), T_8) → F_9
  226. Rotate(P_5, (-α), S_8) → G_9
  227. Rotate(N_5, (-α), R_8) → H_9
  228. Rotate(L_5, (-α), P_8) → I_9
  229. Rotate(Q_7, (-α), O_8) → J_9
  230. Rotate(M_7, (-α), M_8) → K_9
  231. Rotate(O_7, (-α), N_8) → L_9
  232. Rotate(I_7, (-α), B_9) → M_9
  233. Rotate(B_7, (-α), K_8) → N_9
  234. Rotate(Z_6, (-α), H_8) → O_9
  235. Rotate(R_6, (-α), E_8) → Q_9
  236. Rotate(Q_4, (-α), A_8) → R_9
  237. CustomSquare(Z_5, C_9) → S_9, T_9, a_{15}, b_{15}, i_{15}, j_{15}, poly64
  238. CustomSquare(C_9, W_5) → U_9, V_9, l_{15}, m_{15}, n_{15}, a_{16}, poly65
  239. CustomSquare(V_5, D_9) → W_9, Z_9, b_{16}, i_{16}, j_{16}, l_{16}, poly66
  240. CustomSquare(D_9, U_5) → A_{10}, B_{10}, m_{16}, n_{16}, a_{17}, b_{17}, poly67
  241. CustomSquare(T_5, E_9) → C_{10}, D_{10}, f_{17}, g_{17}, h_{17}, i_{17}, poly68
  242. CustomSquare(E_9, S_5) → E_{10}, F_{10}, j_{17}, k_{17}, l_{17}, m_{17}, poly69
  243. CustomSquare(R_5, F_9) → G_{10}, H_{10}, n_{17}, p_{17}, q_{17}, r_{17}, poly70
  244. CustomSquare(F_9, Q_5) → I_{10}, J_{10}, s_{17}, t_{17}, a_{18}, b_{18}, poly71
  245. CustomSquare(P_5, G_9) → K_{10}, L_{10}, c_{18}, d_{18}, e_{18}, f_{18}, poly72
  246. CustomSquare(G_9, O_5) → M_{10}, N_{10}, g_{18}, h_{18}, i_{18}, j_{18}, poly73
  247. CustomSquare(N_5, H_9) → O_{10}, P_{10}, k_{18}, l_{18}, m_{18}, n_{18}, poly74
  248. CustomSquare(H_9, M_5) → Q_{10}, R_{10}, p_{18}, q_{18}, r_{18}, s_{18}, poly75
  249. CustomSquare(L_5, I_9) → S_{10}, T_{10}, t_{18}, a_{19}, b_{19}, c_{19}, poly76
  250. CustomSquare(I_9, K_5) → U_{10}, V_{10}, d_{19}, e_{19}, f_{19}, g_{19}, poly77
  251. CustomSquare(Q_7, J_9) → W_{10}, Z_{10}, h_{19}, i_{19}, j_{19}, k_{19}, poly78
  252. CustomSquare(J_9, P_7) → A_{11}, B_{11}, l_{19}, m_{19}, n_{19}, p_{19}, poly79
  253. CustomSquare(O_7, L_9) → C_{11}, D_{11}, q_{19}, r_{19}, s_{19}, t_{19}, poly80
  254. CustomSquare(L_9, N_7) → E_{11}, F_{11}, a_{20}, b_{20}, c_{20}, d_{20}, poly81
  255. CustomSquare(M_7, K_9) → G_{11}, H_{11}, e_{20}, f_{20}, g_{20}, h_{20}, poly82
  256. CustomSquare(K_9, L_7) → I_{11}, J_{11}, i_{20}, j_{20}, k_{20}, l_{20}, poly83
  257. CustomSquare(B_7, N_9) → K_{11}, L_{11}, m_{20}, n_{20}, p_{20}, q_{20}, poly84
  258. CustomSquare(I_7, M_9) → M_{11}, N_{11}, r_{20}, s_{20}, t_{20}, a_{21}, poly85
  259. CustomSquare(M_9, H_7) → O_{11}, P_{11}, b_{21}, c_{21}, d_{21}, e_{21}, poly86
  260. CustomSquare(N_9, A_7) → Q_{11}, R_{11}, f_{21}, g_{21}, h_{21}, i_{21}, poly87
  261. CustomSquare(Z_6, O_9) → S_{11}, T_{11}, j_{21}, k_{21}, l_{21}, m_{21}, poly88
  262. CustomSquare(O_9, W_6) → U_{11}, V_{11}, n_{21}, p_{21}, q_{21}, r_{21}, poly89
  263. CustomSquare(R_6, Q_9) → C_{12}, D_{12}, g_{22}, h_{22}, i_{22}, j_{22}, poly92
  264. CustomSquare(Q_9, Q_6) → E_{12}, F_{12}, k_{22}, l_{22}, m_{22}, n_{22}, poly93
  265. CustomSquare(Q_4, R_9) → G_{12}, H_{12}, p_{22}, q_{22}, r_{22}, s_{22}, poly94
  266. CustomSquare(R_9, P_4) → I_{12}, J_{12}, t_{22}, a_{23}, b_{23}, c_{23}, poly95
  267. Circle(I_8, D_7) → d_{23}
  268. Circle(J_8, E_7) → e_{23}
  269. Circle(L_8, K_7) → f_{23}
  270. Circle(Q_8, J_5) → g_{23}
  271. Rotate(C_4, (-α), R_7) → K_{12}
  272. Rotate(E_4, (-α), S_7) → L_{12}
  273. Rotate(G_4, (-α), T_7) → M_{12}
  274. Rotate(I_4, (-α), U_7) → N_{12}
  275. Rotate(K_4, (-α), V_7) → O_{12}
  276. Rotate(M_4, (-α), W_7) → P_{12}
  277. Rotate(O_4, (-α), Z_7) → Q_{12}
  278. Circle(B_8, L_6) → h_{23}
  279. Rotate(L_6, (-α), B_8) → R_{12}
  280. Rotate(N_6, (-α), C_8) → S_{12}
  281. Rotate(T_6, (-α), F_8) → U_{12}
  282. Rotate(D_7, (-α), I_8) → V_{12}
  283. Rotate(E_7, (-α), J_8) → W_{12}
  284. Rotate(G_7, (-α), A_9) → Z_{12}
  285. Rotate(K_7, (-α), L_8) → A_{13}
  286. Rotate(J_5, (-α), Q_8) → B_{13}
  287. CustomSquare(C_4, K_{12}) → C_{13}, D_{13}, i_{23}, j_{23}, k_{23}, l_{23}, poly96
  288. CustomSquare(K_{12}, B_4) → E_{13}, F_{13}, m_{23}, n_{23}, p_{23}, q_{23}, poly97
  289. CustomSquare(E_4, L_{12}) → G_{13}, H_{13}, r_{23}, s_{23}, t_{23}, a_{24}, poly98
  290. CustomSquare(L_{12}, D_4) → I_{13}, J_{13}, b_{24}, c_{24}, d_{24}, e_{24}, poly99
  291. CustomSquare(G_4, M_{12}) → K_{13}, L_{13}, f_{24}, g_{24}, h_{24}, i_{24}, poly100
  292. CustomSquare(M_{12}, F_4) → M_{13}, N_{13}, j_{24}, k_{24}, l_{24}, m_{24}, poly101
  293. CustomSquare(I_4, N_{12}) → O_{13}, P_{13}, n_{24}, p_{24}, q_{24}, r_{24}, poly102
  294. CustomSquare(N_{12}, H_4) → Q_{13}, R_{13}, s_{24}, t_{24}, a_{25}, b_{25}, poly103
  295. CustomSquare(K_4, O_{12}) → S_{13}, T_{13}, c_{25}, d_{25}, e_{25}, f_{25}, poly104
  296. CustomSquare(O_{12}, J_4) → U_{13}, V_{13}, g_{25}, h_{25}, i_{25}, j_{25}, poly105
  297. CustomSquare(M_4, P_{12}) → W_{13}, Z_{13}, k_{25}, l_{25}, m_{25}, n_{25}, poly106
  298. CustomSquare(P_{12}, L_4) → A_{14}, B_{14}, p_{25}, q_{25}, r_{25}, s_{25}, poly107
  299. CustomSquare(O_4, Q_{12}) → C_{14}, D_{14}, t_{25}, a_{26}, b_{26}, c_{26}, poly108
  300. CustomSquare(Q_{12}, N_4) → E_{14}, F_{14}, d_{26}, e_{26}, f_{26}, g_{26}, poly109
  301. CustomSquare(L_6, R_{12}) → G_{14}, H_{14}, h_{26}, i_{26}, j_{26}, k_{26}, poly110
  302. CustomSquare(R_{12}, K_6) → I_{14}, J_{14}, l_{26}, m_{26}, n_{26}, p_{26}, poly111
  303. CustomSquare(N_6, S_{12}) → K_{14}, L_{14}, q_{26}, r_{26}, s_{26}, t_{26}, poly112
  304. CustomSquare(S_{12}, M_6) → M_{14}, N_{14}, a_{27}, b_{27}, c_{27}, d_{27}, poly113
  305. CustomSquare(T_6, U_{12}) → S_{14}, T_{14}, m_{27}, n_{27}, p_{27}, q_{27}, poly116
  306. CustomSquare(U_{12}, S_6) → U_{14}, V_{14}, r_{27}, s_{27}, t_{27}, a_{28}, poly117
  307. CustomSquare(D_7, V_{12}) → W_{14}, Z_{14}, b_{28}, c_{28}, d_{28}, e_{28}, poly118
  308. CustomSquare(V_{12}, C_7) → A_{15}, B_{15}, f_{28}, g_{28}, h_{28}, i_{28}, poly119
  309. CustomSquare(E_7, W_{12}) → C_{15}, D_{15}, j_{28}, k_{28}, l_{28}, m_{28}, poly120
  310. CustomSquare(W_{12}, E_6) → E_{15}, F_{15}, n_{28}, p_{28}, q_{28}, r_{28}, poly121
  311. CustomSquare(G_7, Z_{12}) → G_{15}, H_{15}, s_{28}, t_{28}, a_{29}, b_{29}, poly122
  312. CustomSquare(Z_{12}, F_7) → I_{15}, J_{15}, c_{29}, d_{29}, e_{29}, f_{29}, poly123
  313. CustomSquare(K_7, A_{13}) → K_{15}, L_{15}, g_{29}, h_{29}, i_{29}, j_{29}, poly124
  314. CustomSquare(A_{13}, J_7) → M_{15}, N_{15}, k_{29}, l_{29}, m_{29}, n_{29}, poly125
  315. CustomSquare(J_5, B_{13}) → O_{15}, P_{15}, p_{29}, q_{29}, r_{29}, s_{29}, poly126
  316. CustomSquare(B_{13}, I_5) → Q_{15}, R_{15}, t_{29}, a_{30}, b_{30}, c_{30}, poly127
  317. Midpoint(k_{23}) → S_{15}
  318. Midpoint(p_{23}) → T_{15}
  319. Midpoint(t_{23}) → U_{15}
  320. Midpoint(d_{24}) → V_{15}
  321. Midpoint(h_{24}) → W_{15}
  322. Midpoint(l_{24}) → Z_{15}
  323. Circle(S_{15}, D_{13}) → d_{30}
  324. Circle(T_{15}, F_{13}) → e_{30}
  325. Circle(U_{15}, H_{13}) → f_{30}
  326. Circle(V_{15}, I_{13}) → g_{30}
  327. Circle(W_{15}, L_{13}) → h_{30}
  328. Circle(Z_{15}, M_{13}) → k_{30}
  329. Rotate(D_{13}, (-α), S_{15}) → A_{16}
  330. Rotate(F_{13}, (-α), T_{15}) → B_{16}
  331. Rotate(H_{13}, (-α), U_{15}) → C_{16}
  332. Rotate(J_{13}, (-α), V_{15}) → D_{16}
  333. Rotate(L_{13}, (-α), W_{15}) → E_{16}
  334. Rotate(N_{13}, (-α), Z_{15}) → F_{16}
  335. CustomSquare(D_{13}, A_{16}) → G_{16}, H_{16}, i_{30}, j_{30}, l_{30}, m_{30}, poly128
  336. CustomSquare(A_{16}, C_{13}) → I_{16}, J_{16}, n_{30}, p_{30}, q_{30}, r_{30}, poly129
  337. CustomSquare(F_{13}, B_{16}) → K_{16}, L_{16}, s_{30}, t_{30}, a_{31}, b_{31}, poly130
  338. CustomSquare(B_{16}, E_{13}) → M_{16}, N_{16}, c_{31}, d_{31}, e_{31}, f_{31}, poly131
  339. CustomSquare(H_{13}, C_{16}) → O_{16}, P_{16}, g_{31}, h_{31}, i_{31}, j_{31}, poly132
  340. CustomSquare(C_{16}, G_{13}) → Q_{16}, R_{16}, k_{31}, l_{31}, m_{31}, n_{31}, poly133
  341. CustomSquare(J_{13}, D_{16}) → S_{16}, T_{16}, p_{31}, q_{31}, r_{31}, s_{31}, poly134
  342. Point(g_{30}) → U_{16}
  343. CustomSquare(U_{16}, I_{13}) → V_{16}, W_{16}, t_{31}, a_{32}, b_{32}, c_{32}, poly135
  344. CustomSquare(L_{13}, E_{16}) → Z_{16}, A_{17}, d_{32}, e_{32}, f_{32}, g_{32}, poly136
  345. CustomSquare(E_{16}, K_{13}) → B_{17}, C_{17}, h_{32}, i_{32}, j_{32}, k_{32}, poly137
  346. CustomSquare(N_{13}, F_{16}) → D_{17}, E_{17}, l_{32}, m_{32}, n_{32}, p_{32}, poly138
  347. CustomSquare(F_{16}, M_{13}) → F_{17}, G_{17}, q_{32}, r_{32}, s_{32}, t_{32}, poly139
  348. Midpoint(q_{24}) → H_{17}
  349. Midpoint(a_{25}) → I_{17}
  350. Midpoint(i_{25}) → K_{17}
  351. Midpoint(m_{25}) → L_{17}
  352. Midpoint(r_{25}) → M_{17}
  353. Circle(H_{17}, P_{13}) → c_{33}
  354. Circle(I_{17}, R_{13}) → d_{33}
  355. Midpoint(e_{25}) → N_{17}
  356. Circle(N_{17}, T_{13}) → e_{33}
  357. Circle(K_{17}, U_{13}) → f_{33}
  358. Circle(L_{17}, W_{13}) → g_{33}
  359. Circle(M_{17}, A_{14}) → h_{33}
  360. Rotate(P_{13}, (-α), H_{17}) → J_{17}
  361. Rotate(T_{13}, (-α), N_{17}) → O_{17}
  362. Rotate(V_{13}, (-α), K_{17}) → P_{17}
  363. Rotate(Z_{13}, (-α), L_{17}) → Q_{17}
  364. Rotate(B_{14}, (-α), M_{17}) → R_{17}
  365. CustomSquare(P_{13}, J_{17}) → S_{17}, T_{17}, a_{33}, b_{33}, i_{33}, j_{33}, poly140
  366. CustomSquare(J_{17}, O_{13}) → U_{17}, V_{17}, k_{33}, l_{33}, m_{33}, n_{33}, poly141
  367. CustomSquare(T_{13}, O_{17}) → W_{17}, Z_{17}, p_{33}, q_{33}, r_{33}, s_{33}, poly142
  368. CustomSquare(O_{17}, S_{13}) → A_{18}, B_{18}, t_{33}, a_{34}, b_{34}, c_{34}, poly143
  369. CustomSquare(V_{13}, P_{17}) → C_{18}, D_{18}, d_{34}, e_{34}, f_{34}, g_{34}, poly144
  370. CustomSquare(P_{17}, U_{13}) → E_{18}, F_{18}, h_{34}, i_{34}, j_{34}, k_{34}, poly145
  371. Rotate(R_{13}, (-α), I_{17}) → G_{18}
  372. CustomSquare(R_{13}, G_{18}) → H_{18}, I_{18}, l_{34}, m_{34}, n_{34}, p_{34}, poly146
  373. CustomSquare(G_{18}, Q_{13}) → J_{18}, K_{18}, q_{34}, r_{34}, s_{34}, t_{34}, poly147
  374. CustomSquare(Z_{13}, Q_{17}) → L_{18}, M_{18}, a_{35}, b_{35}, c_{35}, d_{35}, poly148
  375. CustomSquare(Q_{17}, W_{13}) → N_{18}, O_{18}, e_{35}, f_{35}, g_{35}, h_{35}, poly149
  376. CustomSquare(B_{14}, R_{17}) → P_{18}, Q_{18}, i_{35}, j_{35}, k_{35}, l_{35}, poly150
  377. CustomSquare(R_{17}, A_{14}) → R_{18}, S_{18}, m_{35}, n_{35}, p_{35}, q_{35}, poly151
  378. Midpoint(b_{26}) → T_{18}
  379. Midpoint(f_{26}) → U_{18}
  380. Midpoint(n_{26}) → V_{18}
  381. Midpoint(j_{26}) → W_{18}
  382. Midpoint(r_{22}) → Z_{18}
  383. Midpoint(c_{27}) → A_{19}
  384. Midpoint(b_{23}) → B_{19}
  385. Circle(T_{18}, D_{14}) → r_{35}
  386. Circle(U_{18}, F_{14}) → s_{35}
  387. Circle(Z_{18}, H_{12}) → t_{35}
  388. Circle(B_{19}, J_{12}) → c_{36}
  389. Rotate(D_{14}, (-α), T_{18}) → C_{19}
  390. Rotate(F_{14}, (-α), U_{18}) → D_{19}
  391. Rotate(H_{12}, (-α), Z_{18}) → E_{19}
  392. Rotate(J_{12}, (-α), B_{19}) → F_{19}
  393. CustomSquare(D_{14}, C_{19}) → G_{19}, H_{19}, a_{36}, b_{36}, d_{36}, e_{36}, poly152
  394. CustomSquare(C_{19}, C_{14}) → I_{19}, J_{19}, f_{36}, g_{36}, h_{36}, i_{36}, poly153
  395. CustomSquare(F_{14}, D_{19}) → K_{19}, L_{19}, j_{36}, k_{36}, l_{36}, m_{36}, poly154
  396. CustomSquare(D_{19}, E_{14}) → M_{19}, N_{19}, n_{36}, p_{36}, q_{36}, r_{36}, poly155
  397. CustomSquare(H_{12}, E_{19}) → O_{19}, P_{19}, s_{36}, t_{36}, a_{37}, b_{37}, poly156
  398. CustomSquare(E_{19}, G_{12}) → Q_{19}, R_{19}, c_{37}, d_{37}, e_{37}, f_{37}, poly157
  399. CustomSquare(J_{12}, F_{19}) → S_{19}, T_{19}, g_{37}, h_{37}, i_{37}, j_{37}, poly158
  400. CustomSquare(F_{19}, I_{12}) → U_{19}, V_{19}, k_{37}, l_{37}, m_{37}, n_{37}, poly159
  401. Midpoint(s_{26}) → W_{19}
  402. Circle(W_{18}, H_{14}) → p_{37}
  403. Circle(V_{18}, J_{14}) → q_{37}
  404. Circle(W_{19}, L_{14}) → r_{37}
  405. Circle(A_{19}, M_{14}) → s_{37}
  406. Rotate(H_{14}, (-α), W_{18}) → Z_{19}
  407. Rotate(J_{14}, (-α), V_{18}) → A_{20}
  408. Rotate(L_{14}, (-α), W_{19}) → B_{20}
  409. Rotate(N_{14}, (-α), A_{19}) → C_{20}
  410. CustomSquare(H_{14}, Z_{19}) → D_{20}, E_{20}, t_{37}, a_{38}, b_{38}, c_{38}, poly160
  411. CustomSquare(Z_{19}, G_{14}) → F_{20}, G_{20}, d_{38}, e_{38}, f_{38}, g_{38}, poly161
  412. CustomSquare(J_{14}, A_{20}) → H_{20}, I_{20}, h_{38}, i_{38}, j_{38}, k_{38}, poly162
  413. CustomSquare(A_{20}, I_{14}) → J_{20}, K_{20}, l_{38}, m_{38}, n_{38}, p_{38}, poly163
  414. CustomSquare(L_{14}, B_{20}) → L_{20}, M_{20}, q_{38}, r_{38}, s_{38}, t_{38}, poly164
  415. CustomSquare(B_{20}, K_{14}) → N_{20}, O_{20}, a_{39}, b_{39}, c_{39}, d_{39}, poly165
  416. CustomSquare(N_{14}, C_{20}) → P_{20}, Q_{20}, e_{39}, f_{39}, g_{39}, h_{39}, poly166
  417. CustomSquare(C_{20}, M_{14}) → R_{20}, S_{20}, i_{39}, j_{39}, k_{39}, l_{39}, poly167
  418. Midpoint(d_{12}) → D_8
  419. Circle(D_8, P_6) → e_{16}
  420. Rotate(P_6, (-α), D_8) → T_{12}
  421. CustomSquare(P_6, T_{12}) → O_{14}, P_{14}, e_{27}, f_{27}, g_{27}, h_{27}, poly114
  422. CustomSquare(T_{12}, O_6) → Q_{14}, R_{14}, i_{27}, j_{27}, k_{27}, l_{27}, poly115
  423. Midpoint(g_{27}) → T_{20}
  424. Midpoint(k_{27}) → U_{20}
  425. Midpoint(i_{22}) → V_{20}
  426. Midpoint(m_{22}) → W_{20}
  427. Midpoint(p_{27}) → Z_{20}
  428. Midpoint(t_{27}) → A_{21}
  429. Circle(T_{20}, P_{14}) → p_{39}
  430. Circle(U_{20}, R_{14}) → q_{39}
  431. Rotate(P_{14}, (-α), T_{20}) → B_{21}
  432. Rotate(R_{14}, (-α), U_{20}) → C_{21}
  433. Circle(V_{20}, D_{12}) → r_{39}
  434. Circle(Z_{20}, S_{14}) → s_{39}
  435. Circle(A_{21}, V_{14}) → t_{39}
  436. Rotate(T_{14}, (-α), Z_{20}) → D_{21}
  437. Rotate(V_{14}, (-α), A_{21}) → E_{21}
  438. Rotate(D_{12}, (-α), V_{20}) → F_{21}
  439. Circle(W_{20}, F_{12}) → c_{40}
  440. Rotate(F_{12}, (-α), W_{20}) → G_{21}
  441. CustomSquare(P_{14}, B_{21}) → H_{21}, I_{21}, m_{39}, n_{39}, a_{40}, b_{40}, poly168
  442. CustomSquare(B_{21}, O_{14}) → J_{21}, K_{21}, d_{40}, e_{40}, f_{40}, g_{40}, poly169
  443. CustomSquare(R_{14}, C_{21}) → L_{21}, M_{21}, h_{40}, i_{40}, j_{40}, k_{40}, poly170
  444. CustomSquare(C_{21}, Q_{14}) → N_{21}, O_{21}, l_{40}, m_{40}, n_{40}, p_{40}, poly171
  445. CustomSquare(D_{12}, F_{21}) → P_{21}, Q_{21}, q_{40}, r_{40}, s_{40}, t_{40}, poly172
  446. CustomSquare(F_{21}, C_{12}) → R_{21}, S_{21}, a_{41}, b_{41}, c_{41}, d_{41}, poly173
  447. CustomSquare(T_{14}, D_{21}) → T_{21}, U_{21}, e_{41}, f_{41}, g_{41}, h_{41}, poly174
  448. CustomSquare(D_{21}, S_{14}) → V_{21}, W_{21}, i_{41}, j_{41}, k_{41}, l_{41}, poly175
  449. CustomSquare(F_{12}, G_{21}) → Z_{21}, A_{22}, m_{41}, n_{41}, p_{41}, q_{41}, poly176
  450. CustomSquare(G_{21}, E_{12}) → B_{22}, C_{22}, r_{41}, s_{41}, t_{41}, a_{42}, poly177
  451. CustomSquare(V_{14}, E_{21}) → D_{22}, E_{22}, b_{42}, c_{42}, d_{42}, e_{42}, poly178
  452. CustomSquare(E_{21}, U_{14}) → F_{22}, G_{22}, f_{42}, g_{42}, h_{42}, i_{42}, poly179
  453. Midpoint(a_{29}) → J_{22}
  454. Midpoint(e_{29}) → K_{22}
  455. Midpoint(t_{20}) → L_{22}
  456. Midpoint(l_{21}) → M_{22}
  457. Midpoint(q_{21}) → N_{22}
  458. Circle(K_{22}, J_{15}) → q_{42}
  459. Circle(J_{22}, H_{15}) → r_{42}
  460. Circle(M_{22}, T_{11}) → s_{42}
  461. Circle(N_{22}, V_{11}) → t_{42}
  462. Rotate(V_6, (-α), G_8) → P_9
  463. Rotate(J_{15}, (-α), K_{22}) → W_{11}
  464. Rotate(H_{15}, (-α), J_{22}) → Z_{11}
  465. CustomSquare(V_6, P_9) → A_{12}, B_{12}, s_{21}, t_{21}, a_{22}, b_{22}, poly90
  466. CustomSquare(P_9, U_6) → H_{22}, I_{22}, c_{22}, d_{22}, e_{22}, f_{22}, poly91
  467. CustomSquare(H_{15}, Z_{11}) → O_{22}, P_{22}, j_{42}, k_{42}, l_{42}, m_{42}, poly180
  468. CustomSquare(Z_{11}, G_{15}) → Q_{22}, R_{22}, n_{42}, p_{42}, a_{43}, b_{43}, poly181
  469. CustomSquare(J_{15}, W_{11}) → S_{22}, T_{22}, c_{43}, d_{43}, e_{43}, f_{43}, poly182
  470. CustomSquare(W_{11}, I_{15}) → U_{22}, V_{22}, g_{43}, h_{43}, i_{43}, j_{43}, poly183
  471. Rotate(T_{11}, (-α), M_{22}) → W_{22}
  472. Rotate(V_{11}, (-α), N_{22}) → Z_{22}
  473. Midpoint(d_{21}) → A_{23}
  474. Midpoint(m_{29}) → B_{23}
  475. Midpoint(i_{29}) → C_{23}
  476. Midpoint(p_{20}) → D_{23}
  477. Midpoint(h_{21}) → E_{23}
  478. Midpoint(q_{28}) → F_{23}
  479. Midpoint(l_{28}) → G_{23}
  480. Midpoint(h_{28}) → H_{23}
  481. Midpoint(d_{28}) → I_{23}
  482. Circle(L_{22}, N_{11}) → k_{43}
  483. Circle(A_{23}, P_{11}) → p_{43}
  484. Circle(F_{23}, E_{15}) → q_{43}
  485. Circle(G_{23}, C_{15}) → r_{43}
  486. Circle(H_{23}, A_{15}) → s_{43}
  487. Circle(I_{23}, Z_{14}) → t_{43}
  488. Circle(D_{23}, L_{11}) → c_{44}
  489. Circle(C_{23}, L_{15}) → d_{44}
  490. Circle(B_{23}, N_{15}) → e_{44}
  491. Rotate(N_{11}, (-α), L_{22}) → J_{23}
  492. Rotate(P_{11}, (-α), A_{23}) → K_{23}
  493. Rotate(L_{11}, (-α), D_{23}) → L_{23}
  494. Rotate(F_{15}, (-α), F_{23}) → M_{23}
  495. CustomSquare(T_{11}, W_{22}) → N_{23}, O_{23}, l_{43}, m_{43}, n_{43}, a_{44}, poly184
  496. CustomSquare(W_{22}, S_{11}) → P_{23}, Q_{23}, b_{44}, f_{44}, g_{44}, h_{44}, poly185
  497. CustomSquare(V_{11}, Z_{22}) → R_{23}, S_{23}, i_{44}, j_{44}, k_{44}, l_{44}, poly186
  498. CustomSquare(Z_{22}, U_{11}) → T_{23}, U_{23}, m_{44}, n_{44}, p_{44}, q_{44}, poly187
  499. CustomSquare(N_{11}, J_{23}) → V_{23}, W_{23}, r_{44}, s_{44}, t_{44}, a_{45}, poly188
  500. CustomSquare(J_{23}, M_{11}) → Z_{23}, A_{24}, b_{45}, c_{45}, d_{45}, e_{45}, poly189
  501. CustomSquare(P_{11}, K_{23}) → B_{24}, C_{24}, f_{45}, g_{45}, h_{45}, i_{45}, poly190
  502. CustomSquare(K_{23}, O_{11}) → D_{24}, E_{24}, j_{45}, k_{45}, l_{45}, m_{45}, poly191
  503. CustomSquare(L_{11}, L_{23}) → F_{24}, G_{24}, n_{45}, p_{45}, q_{45}, r_{45}, poly192
  504. CustomSquare(L_{23}, K_{11}) → H_{24}, I_{24}, s_{45}, t_{45}, a_{46}, b_{46}, poly193
  505. CustomSquare(F_{15}, M_{23}) → J_{24}, K_{24}, c_{46}, d_{46}, e_{46}, f_{46}, poly194
  506. CustomSquare(M_{23}, E_{15}) → L_{24}, M_{24}, g_{46}, h_{46}, i_{46}, j_{46}, poly195
  507. Rotate(D_{15}, (-α), G_{23}) → N_{24}
  508. Rotate(B_{15}, (-α), H_{23}) → O_{24}
  509. Rotate(Z_{14}, (-α), I_{23}) → P_{24}
  510. Rotate(N_{15}, (-α), B_{23}) → Q_{24}
  511. Rotate(L_{15}, (-α), C_{23}) → R_{24}
  512. CustomSquare(Z_{14}, P_{24}) → S_{24}, T_{24}, k_{46}, l_{46}, m_{46}, n_{46}, poly196
  513. CustomSquare(P_{24}, W_{14}) → U_{24}, V_{24}, p_{46}, q_{46}, r_{46}, s_{46}, poly197
  514. CustomSquare(B_{15}, O_{24}) → W_{24}, Z_{24}, t_{46}, a_{47}, b_{47}, c_{47}, poly198
  515. CustomSquare(O_{24}, A_{15}) → A_{25}, B_{25}, d_{47}, e_{47}, f_{47}, g_{47}, poly199
  516. CustomSquare(D_{15}, N_{24}) → C_{25}, D_{25}, h_{47}, i_{47}, j_{47}, k_{47}, poly200
  517. CustomSquare(N_{24}, C_{15}) → E_{25}, F_{25}, l_{47}, m_{47}, n_{47}, p_{47}, poly201
  518. CustomSquare(N_{15}, Q_{24}) → G_{25}, H_{25}, q_{47}, r_{47}, s_{47}, t_{47}, poly202
  519. CustomSquare(Q_{24}, M_{15}) → I_{25}, J_{25}, a_{48}, b_{48}, c_{48}, d_{48}, poly203
  520. CustomSquare(L_{15}, R_{24}) → K_{25}, L_{25}, e_{48}, f_{48}, g_{48}, h_{48}, poly204
  521. CustomSquare(R_{24}, K_{15}) → M_{25}, N_{25}, i_{48}, j_{48}, k_{48}, l_{48}, poly205
  522. Midpoint(n_{15}) → O_{25}
  523. Midpoint(i_{15}) → P_{25}
  524. Midpoint(a_{17}) → Q_{25}
  525. Midpoint(j_{16}) → R_{25}
  526. Circle(Q_{25}, B_{10}) → p_{48}
  527. Circle(R_{25}, Z_9) → q_{48}
  528. Circle(P_{25}, T_9) → r_{48}
  529. Circle(O_{25}, U_9) → s_{48}
  530. Rotate(V_9, (-α), O_{25}) → S_{25}
  531. Rotate(T_9, (-α), P_{25}) → T_{25}
  532. Rotate(Z_9, (-α), R_{25}) → U_{25}
  533. Rotate(B_{10}, (-α), Q_{25}) → V_{25}
  534. CustomSquare(V_9, S_{25}) → W_{25}, Z_{25}, m_{48}, n_{48}, t_{48}, a_{49}, poly206
  535. CustomSquare(S_{25}, U_9) → A_{26}, B_{26}, b_{49}, c_{49}, d_{49}, e_{49}, poly207
  536. CustomSquare(T_9, T_{25}) → C_{26}, D_{26}, f_{49}, g_{49}, h_{49}, i_{49}, poly208
  537. CustomSquare(T_{25}, S_9) → E_{26}, F_{26}, j_{49}, k_{49}, l_{49}, m_{49}, poly209
  538. CustomSquare(B_{10}, V_{25}) → G_{26}, H_{26}, n_{49}, p_{49}, q_{49}, r_{49}, poly210
  539. CustomSquare(V_{25}, A_{10}) → I_{26}, J_{26}, s_{49}, t_{49}, a_{50}, b_{50}, poly211
  540. CustomSquare(Z_9, U_{25}) → K_{26}, L_{26}, c_{50}, d_{50}, e_{50}, f_{50}, poly212
  541. CustomSquare(U_{25}, W_9) → M_{26}, N_{26}, g_{50}, h_{50}, i_{50}, j_{50}, poly213
  542. Midpoint(l_{17}) → O_{26}
  543. Midpoint(h_{17}) → P_{26}
  544. Midpoint(a_{18}) → Q_{26}
  545. Midpoint(q_{17}) → R_{26}
  546. Midpoint(e_{18}) → S_{26}
  547. Midpoint(i_{18}) → T_{26}
  548. Circle(O_{26}, F_{10}) → k_{50}
  549. Circle(P_{26}, D_{10}) → p_{50}
  550. Circle(Q_{26}, J_{10}) → q_{50}
  551. Circle(R_{26}, G_{10}) → r_{50}
  552. Circle(S_{26}, L_{10}) → s_{50}
  553. Circle(T_{26}, N_{10}) → t_{50}
  554. Rotate(F_{10}, (-α), O_{26}) → U_{26}
  555. Rotate(D_{10}, (-α), P_{26}) → V_{26}
  556. Rotate(J_{10}, (-α), Q_{26}) → W_{26}
  557. Rotate(H_{10}, (-α), R_{26}) → Z_{26}
  558. Rotate(L_{10}, (-α), S_{26}) → A_{27}
  559. Rotate(N_{10}, (-α), T_{26}) → B_{27}
  560. CustomSquare(N_{10}, B_{27}) → C_{27}, D_{27}, l_{50}, m_{50}, n_{50}, a_{51}, poly214
  561. CustomSquare(B_{27}, M_{10}) → E_{27}, F_{27}, b_{51}, c_{51}, d_{51}, e_{51}, poly215
  562. CustomSquare(L_{10}, A_{27}) → G_{27}, H_{27}, f_{51}, g_{51}, h_{51}, i_{51}, poly216
  563. CustomSquare(A_{27}, K_{10}) → I_{27}, J_{27}, j_{51}, k_{51}, l_{51}, m_{51}, poly217
  564. CustomSquare(H_{10}, Z_{26}) → K_{27}, L_{27}, n_{51}, p_{51}, q_{51}, r_{51}, poly218
  565. CustomSquare(Z_{26}, G_{10}) → M_{27}, N_{27}, s_{51}, t_{51}, a_{52}, b_{52}, poly219
  566. CustomSquare(J_{10}, W_{26}) → O_{27}, P_{27}, c_{52}, d_{52}, e_{52}, f_{52}, poly220
  567. CustomSquare(W_{26}, I_{10}) → Q_{27}, R_{27}, g_{52}, h_{52}, i_{52}, j_{52}, poly221
  568. CustomSquare(D_{10}, V_{26}) → S_{27}, T_{27}, k_{52}, l_{52}, m_{52}, n_{52}, poly222
  569. CustomSquare(V_{26}, C_{10}) → U_{27}, V_{27}, p_{52}, q_{52}, r_{52}, s_{52}, poly223
  570. CustomSquare(F_{10}, U_{26}) → W_{27}, Z_{27}, t_{52}, a_{53}, b_{53}, c_{53}, poly224
  571. CustomSquare(U_{26}, E_{10}) → A_{28}, B_{28}, d_{53}, e_{53}, f_{53}, g_{53}, poly225
  572. Midpoint(r_{18}) → C_{28}
  573. Midpoint(m_{18}) → D_{28}
  574. Midpoint(f_{19}) → E_{28}
  575. Midpoint(b_{19}) → F_{28}
  576. Midpoint(b_{30}) → G_{28}
  577. Circle(C_{28}, R_{10}) → h_{53}
  578. Circle(D_{28}, P_{10}) → k_{53}
  579. Circle(E_{28}, V_{10}) → p_{53}
  580. Circle(F_{28}, T_{10}) → q_{53}
  581. Circle(G_{28}, R_{15}) → r_{53}
  582. Rotate(R_{10}, (-α), C_{28}) → H_{28}
  583. Rotate(V_{10}, (-α), E_{28}) → I_{28}
  584. Rotate(T_{10}, (-α), F_{28}) → J_{28}
  585. Rotate(R_{15}, (-α), G_{28}) → K_{28}
  586. Rotate(P_{10}, (-α), D_{28}) → M_{28}
  587. CustomSquare(R_{15}, K_{28}) → N_{28}, O_{28}, i_{53}, j_{53}, l_{53}, m_{53}, poly226
  588. CustomSquare(K_{28}, Q_{15}) → P_{28}, Q_{28}, n_{53}, s_{53}, t_{53}, a_{54}, poly227
  589. CustomSquare(T_{10}, J_{28}) → R_{28}, S_{28}, b_{54}, c_{54}, d_{54}, e_{54}, poly228
  590. CustomSquare(J_{28}, S_{10}) → T_{28}, U_{28}, f_{54}, g_{54}, h_{54}, i_{54}, poly229
  591. CustomSquare(V_{10}, I_{28}) → V_{28}, W_{28}, j_{54}, k_{54}, l_{54}, m_{54}, poly230
  592. CustomSquare(I_{28}, U_{10}) → Z_{28}, A_{29}, n_{54}, p_{54}, q_{54}, r_{54}, poly231
  593. CustomSquare(P_{10}, M_{28}) → B_{29}, C_{29}, s_{54}, t_{54}, a_{55}, b_{55}, poly232
  594. CustomSquare(M_{28}, O_{10}) → D_{29}, E_{29}, c_{55}, d_{55}, e_{55}, f_{55}, poly233
  595. CustomSquare(R_{10}, H_{28}) → F_{29}, G_{29}, g_{55}, h_{55}, i_{55}, j_{55}, poly234
  596. CustomSquare(H_{28}, Q_{10}) → H_{29}, I_{29}, k_{55}, l_{55}, m_{55}, n_{55}, poly235
  597. Circle(E_{23}, R_{11}) → p_{55}
  598. Rotate(R_{11}, (-α), E_{23}) → L_{28}
  599. CustomSquare(R_{11}, L_{28}) → J_{29}, K_{29}, q_{55}, r_{55}, s_{55}, t_{55}, poly236
  600. CustomSquare(L_{28}, Q_{11}) → L_{29}, M_{29}, a_{56}, b_{56}, c_{56}, d_{56}, poly237
  601. Midpoint(g_{20}) → N_{29}
  602. Midpoint(k_{20}) → O_{29}
  603. Midpoint(n_{19}) → P_{29}
  604. Midpoint(j_{19}) → Q_{29}
  605. Midpoint(s_{19}) → R_{29}
  606. Circle(P_{29}, B_{11}) → e_{56}
  607. Circle(Q_{29}, Z_{10}) → f_{56}
  608. Circle(O_{29}, J_{11}) → g_{56}
  609. Circle(N_{29}, G_{11}) → h_{56}
  610. Circle(R_{29}, C_{11}) → k_{56}
  611. Rotate(B_{11}, (-α), P_{29}) → S_{29}
  612. Rotate(Z_{10}, (-α), Q_{29}) → T_{29}
  613. Rotate(D_{11}, (-α), R_{29}) → U_{29}
  614. Rotate(H_{11}, (-α), N_{29}) → V_{29}
  615. Rotate(J_{11}, (-α), O_{29}) → W_{29}
  616. CustomSquare(H_{11}, V_{29}) → Z_{29}, A_{30}, i_{56}, j_{56}, l_{56}, m_{56}, poly238
  617. CustomSquare(V_{29}, G_{11}) → B_{30}, C_{30}, n_{56}, p_{56}, q_{56}, r_{56}, poly239
  618. CustomSquare(J_{11}, W_{29}) → D_{30}, E_{30}, s_{56}, t_{56}, a_{57}, b_{57}, poly240
  619. CustomSquare(W_{29}, I_{11}) → F_{30}, G_{30}, c_{57}, d_{57}, e_{57}, f_{57}, poly241
  620. CustomSquare(D_{11}, U_{29}) → H_{30}, I_{30}, g_{57}, h_{57}, i_{57}, j_{57}, poly242
  621. CustomSquare(U_{29}, C_{11}) → J_{30}, K_{30}, k_{57}, l_{57}, m_{57}, n_{57}, poly243
  622. CustomSquare(S_{29}, A_{11}) → L_{30}, M_{30}, p_{57}, q_{57}, r_{57}, s_{57}, poly244
  623. CustomSquare(B_{11}, S_{29}) → N_{30}, O_{30}, t_{57}, a_{58}, b_{58}, c_{58}, poly245
  624. CustomSquare(T_{29}, W_{10}) → P_{30}, Q_{30}, d_{58}, e_{58}, f_{58}, g_{58}, poly246
  625. CustomSquare(Z_{10}, T_{29}) → R_{30}, S_{30}, h_{58}, i_{58}, j_{58}, k_{58}, poly247

AI Drawing Prompt Reference

Draw a fractal based on the Pythagorean tree, constructed by iterating semicircles and squares. Start with a horizontal segment, add a semicircle above it, and build a square on the segment. Then rotate a point by a fixed angle to create a new square and semicircle on its side. Repeat this process recursively, each time adding smaller squares and semicircles on the rotated sides, forming a branching tree-like pattern. The final image shows multiple levels of nested squares and semicircles, with clear self-similarity and rotational symmetry, suitable for demonstrating fractal geometry.
The prompt above was compiled from the original drawing commands and is for reference only.