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Geometric Construction of a Muqarnas Bursa Decorative Pattern

Geometric Construction of a Muqarnas Bursa Decorative Pattern
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2020-08-03 23:53
CirclePolygonSolid GeometryTransformationGeometric Construction
In collections building muqarnas in GeoGebra
This example demonstrates how to build a Muqarnas-style Bursa (Abdal Mehmet) ornamental geometry using iterative geometric transformations. It highlights the way complex, tile-like decorative structures emerge from repeatable construction rules. The key mathematics includes similarity transformations (dilate/scale), rotation (Rotate), intersection-based construction (Intersect), and assembling polygonal regions (Polygon) from computed vertices. Construction workflow: Rotate is used to reposition a local motif; Intersect finds the key join points between transformed edges so the pieces match precisely; Dilate maps the motif across different scales to create nested structure; Polygon and Segment are then used to form the outlines of the decorative blocks from the resulting points. The script also incorporates square-root based lengths (e.g., LeftSqrt2/UpSqrt2/DownSqrt2/RightSqrt2) and template-like primitives (such as almond/square/rhombus modules) to generate multiple subcomponents, while If supports conditional construction paths. Suitable for advanced middle school through undergraduate geometry modeling and dynamic-geometry lessons, focusing on geometric construction and transformation-driven pattern generation.

GeoGebra Commands & Parameters

  1. Rotate(A, (-(90°)), B) → AB
  2. Rotate(B, 90°, A) → BA
  3. Rotate(B, 135°, A) → BAR
  4. Rotate(B, (-(135°)), A) → ABA
  5. Intersect(Ray[ABA, Rotate[A, 45°, ABA]], Ray[B, Rotate[A, (-(45°)), B]]) → ABAB
  6. Intersect(Ray[A, Rotate[B, 45°, A]], Ray[B, Rotate[A, (-(45°)), B]]) → ABH
  7. Intersect(Ray[A, Rotate[B, 67.5°, A]], Ray[B, Rotate[A, (-(67.5°)), B]]) → ABHR
  8. Intersect(Ray[B, Rotate[A, (-(22.5°)), B]], Ray[BA, Rotate[A, 22.5°, BA]]) → ABL
  9. Rotate(A, (-(45°)), B) → ABR
  10. Intersect(OrthogonalLine[BAR, Line[A, B]], OrthogonalLine[B, Line[A, BAR]]) → ABT
  11. Rotate(B, 135°, A) → BBA
  12. Intersect(Ray[B, Rotate[A, (-(67.5°)), B]], Ray[BBA, Rotate[A, 67.5°, BBA]]) → BAJ
  13. Intersect(OrthogonalLine[BAR, Line[A, BAR]], OrthogonalLine[B, Line[A, B]]) → BARB
  14. Intersect(OrthogonalLine[B, Line[A, B]], OrthogonalLine[BBA, Line[BBA, A]]) → BBAB
  15. Polygon(A, B, AB, BA) → Square1, a, b, ab, ba
  16. Dilate(A, 75, Centroid[Square1]) → A'
  17. Dilate(B, 75, Centroid[Square1]) → B'
  18. Dilate(AB, 75, Centroid[Square1]) → AB'
  19. Dilate(BA, 75, Centroid[Square1]) → BA'
  20. Polygon(Dilate[A, 0.75, Centroid[Square1]], Dilate[B, 0.75, Centroid[Square1]], Dilate[AB, 0.75, Centroid[Square1]], Dilate[BA, 0.75, Centroid[Square1]]) → Square1', f, g, i, j
  21. Segment(A, AB) → k
  22. Segment(B, AB) → l
  23. Segment(BA, AB) → m
  24. Segment(A, BA) → n
  25. Segment(A, B) → p
  26. Polygon(A, B, ABR, BAR) → Rhombus2, a_1, b_1, abr, bar
  27. Dilate(A, 0.75, Centroid[Rhombus2]) → A'_1
  28. Dilate(B, 0.75, Centroid[Rhombus2]) → B'_1
  29. Dilate(ABR, 0.75, Centroid[Rhombus2]) → ABR'
  30. Dilate(BAR, 0.75, Centroid[Rhombus2]) → BAR'
  31. Polygon(A'_1, B'_1, ABR', BAR') → Rhombus2', a'_1, b'_1, abr', bar'
  32. Segment(A, BAR) → r
  33. Segment(B, BAR) → s
  34. Segment(B, ABR) → t
  35. Segment(B, A) → c
  36. Polygon(A, B, BBAB, BBA) → Almond3, a_2, b_2, bbab, bba
  37. Dilate(A, 0.75, Centroid[Almond3]) → A'_2
  38. Dilate(B, 0.75, Centroid[Almond3]) → B'_2
  39. Dilate(BBAB, 0.75, Centroid[Almond3]) → BBAB'
  40. Dilate(BBA, 0.75, Centroid[Almond3]) → BBA'
  41. Polygon(A'_2, B'_2, BBAB', BBA') → Almond3', a'_2, b'_2, bbab', bba'
  42. Segment(A, BBAB) → d
  43. Segment(B, BBAB) → e
  44. Segment(BBA, BBAB) → f_1
  45. Polygon(A, B, ABT, BAR) → SmBiped9, a_3, b_3, abt, g_1
  46. Dilate(A, 0.75, Centroid[SmBiped9]) → A'_3
  47. Dilate(B, 0.75, Centroid[SmBiped9]) → B'_3
  48. Dilate(ABT, 0.75, Centroid[SmBiped9]) → ABT'
  49. Dilate(BAR, 0.75, Centroid[SmBiped9]) → BAR'_1
  50. Polygon(A'_3, B'_3, ABT', BAR'_1) → SmBiped9', a'_3, b'_3, abt', bar'_1
  51. Segment(A, B) → h_1
  52. Segment(A, BAR) → i_1
  53. Segment(A, ABT) → j_1
  54. Polygon(A, B, BAJ, BBA) → Jug4, a_4, b_4, baj, k_1
  55. Dilate(A, 0.75, Centroid[Jug4]) → A'_4
  56. Dilate(B, 0.75, Centroid[Jug4]) → B'_4
  57. Dilate(BAJ, 0.75, Centroid[Jug4]) → BAJ'
  58. Dilate(BBA, 0.75, Centroid[Jug4]) → BBA'_1
  59. Polygon(A'_4, B'_4, BAJ', BBA'_1) → Jug4', a'_4, b'_4, baj', bba'_1
  60. Segment(A, BAJ) → l_1
  61. Segment(BBA, BAJ) → m_1
  62. Segment(B, BAJ) → n_1
  63. Polygon(A, B, ABL, BA) → LBiped10, a_5, b_5, abl, p_1
  64. Dilate(A, 0.75, Centroid[LBiped10]) → A'_5
  65. Dilate(B, 0.75, Centroid[LBiped10]) → B'_5
  66. Dilate(ABL, 0.75, Centroid[LBiped10]) → ABL'
  67. Dilate(BA, 0.75, Centroid[LBiped10]) → BA'_1
  68. Polygon(A'_5, B'_5, ABL', BA'_1) → LBiped10', a'_5, b'_5, abl', ba'_1
  69. Segment(A, B) → q_1
  70. Segment(A, BA) → r_1
  71. Segment(A, ABL) → s_1
  72. Polygon(A, B, ABH) → HSquare5, abh, a_6, b_6
  73. Dilate(A, 0.75, Centroid[HSquare5]) → A'_6
  74. Dilate(B, 0.75, Centroid[HSquare5]) → B'_6
  75. Dilate(ABH, 0.75, Centroid[HSquare5]) → ABH'
  76. Polygon(A'_6, B'_6, ABH') → HSquare5', abh', a'_6, b'_6
  77. Segment(Midpoint[A, B], ABH) → t_1
  78. Segment(A, ABH) → c_1
  79. Segment(B, ABH) → d_1
  80. Polygon(A, B, BA) → HSquare11, e_1, a_7, b_7
  81. Dilate(A, 0.75, Centroid[HSquare11]) → A'_7
  82. Dilate(B, 0.75, Centroid[HSquare11]) → B'_7
  83. Dilate(BA, 0.75, Centroid[HSquare11]) → BA'_2
  84. Polygon(A'_7, B'_7, BA'_2) → HSquare11', ba'_2, a'_7, b'_7
  85. Segment(A, Midpoint[BA, B]) → f_2
  86. Segment(A, BA) → g_2
  87. Segment(A, B) → h_2
  88. Polygon(A, B, ABHR) → HRhombus6, abhr, a_8, b_8
  89. Dilate(A, 0.75, Centroid[HRhombus6]) → A'_8
  90. Dilate(B, 0.75, Centroid[HRhombus6]) → B'_8
  91. Dilate(ABHR, 0.75, Centroid[HRhombus6]) → ABHR'
  92. Polygon(A'_8, B'_8, ABHR') → HRhombus6', abhr', a'_8, b'_8
  93. Segment(Midpoint[A, B], ABHR) → i_2
  94. Segment(A, ABHR) → j_2
  95. Segment(B, ABHR) → k_2
  96. Polygon(A, B, BAR) → HRhombus12, l_2, a_9, b_9
  97. Dilate(A, 0.75, Centroid[HRhombus12]) → A'_9
  98. Dilate(B, 0.75, Centroid[HRhombus12]) → B'_9
  99. Dilate(BAR, 0.75, Centroid[HRhombus12]) → BAR'_2
  100. Polygon(A'_9, B'_9, BAR'_2) → HRhombus12', bar'_2, a'_9, b'_9
  101. Segment(A, Midpoint[BAR, B]) → m_2
  102. Segment(A, BAR) → n_2
  103. Segment(A, B) → p_2
  104. Polygon(ABA, A, B, ABAB) → SmBiped13, aba, a_{10}, b_{10}, abab
  105. Dilate(ABA, 0.75, Centroid[SmBiped13]) → ABA'
  106. Dilate(A, 0.75, Centroid[SmBiped13]) → A'_{10}
  107. Dilate(B, 0.75, Centroid[SmBiped13]) → B'_{10}
  108. Dilate(ABAB, 0.75, Centroid[SmBiped13]) → ABAB'
  109. Polygon(ABA', A'_{10}, B'_{10}, ABAB') → SmBiped13', aba', a'_{10}, b'_{10}, abab'
  110. Segment(ABA, ABAB) → q_2
  111. Segment(A, ABAB) → r_2
  112. Segment(B, ABAB) → s_2
  113. Polygon(A, B, BARB, BAR) → Almond14, a_{11}, b_{11}, barb, t_2
  114. Dilate(A, 0.75, Centroid[Almond14]) → A'_{11}
  115. Dilate(B, 0.75, Centroid[Almond14]) → B'_{11}
  116. Dilate(BARB, 0.75, Centroid[Almond14]) → BARB'
  117. Dilate(BAR, 0.75, Centroid[Almond14]) → BAR'_3
  118. Polygon(A'_{11}, B'_{11}, BARB', BAR'_3) → Almond14', a'_{11}, b'_{11}, barb', bar'_3
  119. Segment(A, B) → c_2
  120. Segment(A, BARB) → d_2
  121. Segment(A, BAR) → e_2
  122. Segment(BAR, ABR) → q
  123. Segment(A, ABR) → g_3
  124. Segment(A, B) → h_3
  125. Segment(A, BAR) → i_3
  126. Polygon(D, E, EE, DD) → achter1, d_3, e_3, ee, dd
  127. Polygon(C, CC, DD, D) → achter2, c_3, cc, j_3, d_4
  128. Polygon(EE, EC, DD) → Square1boven1, k_3, l_3, ec
  129. Polygon(CC, EC, DD) → Square1boven2, m_3, n_3, p_3
  130. Polygon(EE, ECA, DD) → Almond3boven1, q_3, r_3, eca
  131. Polygon(CC, ECA, DD) → Almond3boven2, s_3, t_3, f_4
  132. Polygon(EE, ECJ, DD) → Jug4boven1, g_4, h_4, ecj
  133. Polygon(CC, ECJ, DD) → Jug4boven2, i_4, j_4, k_4
  134. Polygon(CC, DD, CDHS) → HSquare5boven, cdhs, l_4, m_4
  135. Polygon(CC, DD, CDHR) → HRhombusboven, cdhr, n_4, p_4
  136. Polygon(EE, ECSB, DD) → SmBiped2boven1, q_4, r_4, ecsb
  137. Polygon(DD, ECSB, CC) → SmBiped2boven2, s_4, t_4, c_4
  138. Intersect(Line[C, Line[D, E]], Line[E, Line[D, C]]) → CE
  139. Polygon(DU, E, CE) → Square7boven1, ce, du, e_4
  140. Polygon(DU, CE, C) → Square7boven2, c_5, f_5, g_5
  141. Intersect(Line[C, Rotate[D, 45°, Line[C, C + (0, 0, 1)]]], Line[E, Rotate[D, (-(45°)), Line[E, E + (0, 0, 1)]]]) → CESB
  142. Polygon(DU, E, CESB) → SmBiped9boven1, cesb, h_5, e_5
  143. Polygon(DU, CESB, C) → SmBiped9boven2, c_6, i_5, j_5
  144. Intersect(Line[C, Rotate[D, 22.5°, Line[C, C + (0, 0, 1)]]], Line[E, Rotate[D, (-(22.5°)), Line[E, E + (0, 0, 1)]]]) → CELB
  145. Polygon(DU, E, CELB) → LBiped10boven1, celb, k_5, e_6
  146. Polygon(DU, CELB, C) → LBiped10boven2, c_7, l_5, m_5
  147. Intersect(Line[C, Rotate[D, 90°, Line[C, C + (0, 0, 1)]]], Line[E, Rotate[D, (-(90°)), Line[E, E + (0, 0, 1)]]]) → CEA
  148. Polygon(DU, E, CEA) → Almond14onder1, cea, p_5, e_8
  149. Polygon(DU, CEA, C) → Almond14onder2, c_9, q_5, r_5
  150. Left1(F) → G
  151. Left1(G) → H
  152. LeftSqrt2(H) → M
  153. Left1(M) → N
  154. TAlmond14(N, M) → O, P, vierhoek3, vierhoek4, n_6, p_6, q_6, r_6, s_6, t_6
  155. Left1(N) → Q
  156. LeftSqrt2(N) → R
  157. UpSqrt2(R) → S
  158. THSquare5(S, R) → T, driehoek3, driehoek4, d_6, f_7, g_7, h_7, i_7, j_7
  159. THRhombus6(T, Q) → U, driehoek5, driehoek6, k_7, l_7, m_7, n_7, p_7, q_7
  160. Up1(T) → V
  161. TRhombus2(V, T) → W, Z, g_8, vierhoek5, vierhoek6, r_7, s_7, t_7, d_7, e_7, f_8
  162. Up1(Z) → A_1
  163. Left1(Z) → B_1
  164. THSquare5(A_1, B_1) → C_1, driehoek7, driehoek8, h_8, i_8, j_8, k_8, l_8, m_8
  165. Up1(B_1) → D_1
  166. DownSqrt2(D_1) → E_1
  167. TAlmond3(E_1, V) → F_1, G_1, c_8, vierhoek7, vierhoek8, n_8, p_8, q_8, r_8, s_8, t_8
  168. LeftSqrt2(V) → H_1
  169. Right1(H_1) → I_1
  170. TAlmond3(I_1, S) → J_1, K_1, k_9, vierhoek9, vierhoek10, d_8, f_9, g_9, h_9, i_9, j_9
  171. TLBiped10(A_1, Z) → L_1, M_1, s_9, vierhoek11, vierhoek12, l_9, m_9, n_9, p_9, q_9, r_9
  172. Up1(M_1) → N_1
  173. THSquare5(N_1, A_1) → O_1, driehoek9, driehoek10, t_9, d_9, e_9, f_{10}, g_{10}, h_{10}
  174. Left1(N_1) → P_1
  175. RightSqrt2(P_1) → Q_1
  176. TAlmond3(Q_1, N_1) → R_1, S_1, p_{10}, vierhoek13, vierhoek14, i_{10}, j_{10}, k_{10}, l_{10}, m_{10}, n_{10}
  177. TRhombus2(R_1, M_1) → T_1, U_1, e_{10}, vierhoek15, vierhoek16, q_{10}, r_{10}, s_{10}, t_{10}, c_{10}, d_{10}
  178. UpSqrt2(R_1) → V_1
  179. Down1(V_1) → W_1
  180. TAlmond3(W_1, R_1) → Z_1, A_2, l_{11}, vierhoek17, vierhoek18, f_{11}, g_{11}, h_{11}, i_{11}, j_{11}, k_{11}
  181. RightSqrt2(Z_1) → B_2
  182. THSquare5(B_2, Z_1) → C_2, driehoek11, driehoek12, m_{11}, n_{11}, p_{11}, q_{11}, r_{11}, s_{11}
  183. RightSqrt2(B_2) → D_2
  184. THSquare5(D_2, B_2) → E_2, driehoek13, driehoek14, t_{11}, c_{11}, d_{11}, e_{11}, f_{12}, g_{12}
  185. TLBiped10(B_2, U_1) → F_2, G_2, n_{12}, vierhoek19, vierhoek20, h_{12}, i_{12}, j_{12}, k_{12}, l_{12}, m_{12}
  186. Right1(E_2) → H_2
  187. TRhombus2(H_2, E_2) → I_2, J_2, b_{12}, vierhoek21, vierhoek22, p_{12}, q_{12}, r_{12}, s_{12}, t_{12}, a_{12}
  188. UpSqrt2(H_2) → K_2
  189. Down1(K_2) → L_2
  190. TAlmond3(L_2, D_2) → M_2, N_2, i_{13}, vierhoek23, vierhoek24, c_{12}, d_{12}, e_{12}, f_{13}, g_{13}, h_{13}
  191. Up1(J_2) → O_2
  192. Right1(O_2) → P_2
  193. LeftSqrt2(P_2) → Q_2
  194. TAlmond3(Q_2, H_2) → R_2, S_2, q_{13}, vierhoek25, vierhoek26, j_{13}, k_{13}, l_{13}, m_{13}, n_{13}, p_{13}
  195. Right1(J_2) → T_2
  196. THSquare5(T_2, O_2) → U_2, driehoek15, driehoek16, r_{13}, s_{13}, t_{13}, a_{13}, b_{13}, c_{13}
  197. TLBiped10(T_2, J_2) → V_2, W_2, j_{14}, vierhoek27, vierhoek28, d_{13}, e_{13}, f_{14}, g_{14}, h_{14}, i_{14}
  198. Right1(W_2) → Z_2
  199. THSquare5(Z_2, T_2) → A_3, driehoek17, driehoek18, k_{14}, l_{14}, m_{14}, n_{14}, p_{14}, q_{14}
  200. Up1(Z_2) → B_3
  201. DownSqrt2(B_3) → C_3
  202. TAlmond3(C_3, Z_2) → D_3, E_3, d_{14}, vierhoek29, vierhoek30, r_{14}, s_{14}, t_{14}, a_{14}, b_{14}, c_{14}
  203. TRhombus2(D_3, W_2) → F_3, G_3, k_{15}, vierhoek31, vierhoek32, e_{14}, f_{15}, g_{15}, h_{15}, i_{15}, j_{15}
  204. RightSqrt2(D_3) → H_3
  205. Left1(H_3) → I_3
  206. TAlmond3(I_3, D_3) → J_3, K_3, s_{15}, vierhoek33, vierhoek34, l_{15}, m_{15}, n_{15}, p_{15}, q_{15}, r_{15}
  207. DownSqrt2(J_3) → L_3
  208. THSquare5(L_3, J_3) → M_3, driehoek19, driehoek20, t_{15}, a_{15}, b_{15}, c_{15}, d_{15}, e_{15}
  209. LeftSqrt2(L_3) → N_3
  210. Right1(N_3) → O_3
  211. THRhombus6(O_3, G_3) → P_3, driehoek21, driehoek22, f_{16}, g_{16}, h_{16}, i_{16}, j_{16}, k_{16}
  212. TLBiped10(G_3, F_3) → Q_3, R_3, s_{16}, vierhoek35, vierhoek36, l_{16}, m_{16}, n_{16}, p_{16}, q_{16}, r_{16}
  213. TLBiped10(T, N) → S_3, T_3, f_{17}, vierhoek37, vierhoek38, t_{16}, a_{16}, b_{16}, c_{16}, d_{16}, e_{16}
  214. TJug4(Q_3, F_3) → U_3, V_3, m_{17}, vierhoek39, vierhoek40, g_{17}, h_{17}, i_{17}, j_{17}, k_{17}, l_{17}
  215. TJug4(V_2, J_2) → W_3, Z_3, a_{17}, vierhoek41, vierhoek42, n_{17}, p_{17}, q_{17}, r_{17}, s_{17}, t_{17}
  216. TJug4(F_2, U_1) → A_4, B_4, h_{18}, vierhoek43, vierhoek44, b_{17}, c_{17}, d_{17}, e_{17}, f_{18}, g_{18}
  217. TJug4(L_1, Z) → C_4, D_4, p_{18}, vierhoek45, vierhoek46, i_{18}, j_{18}, k_{18}, l_{18}, m_{18}, n_{18}
  218. TJug4(S_3, N) → E_4, F_4, c_{18}, vierhoek47, vierhoek48, q_{18}, r_{18}, s_{18}, t_{18}, a_{18}, b_{18}
  219. TLBiped10(W_2, W_3) → G_4, H_4, j_{19}, vierhoek49, vierhoek50, d_{18}, e_{18}, f_{19}, g_{19}, h_{19}, i_{19}
  220. TLBiped10(J_2, I_2) → I_4, J_4, r_{19}, vierhoek51, vierhoek52, k_{19}, l_{19}, m_{19}, n_{19}, p_{19}, q_{19}
  221. TLBiped10(E_2, A_4) → K_4, L_4, e_{19}, vierhoek53, vierhoek54, s_{19}, t_{19}, a_{19}, b_{19}, c_{19}, d_{19}
  222. TLBiped10(U_1, T_1) → M_4, N_4, l_{20}, vierhoek55, vierhoek56, f_{20}, g_{20}, h_{20}, i_{20}, j_{20}, k_{20}
  223. TLBiped10(M_1, C_4) → O_4, P_4, t_{20}, vierhoek57, vierhoek58, m_{20}, n_{20}, p_{20}, q_{20}, r_{20}, s_{20}
  224. TLBiped10(Z, W) → Q_4, R_4, g_{21}, vierhoek59, vierhoek60, a_{20}, b_{20}, c_{20}, d_{20}, e_{20}, f_{21}
  225. TJug4(G_4, W_3) → S_4, T_4, n_{21}, vierhoek61, vierhoek62, h_{21}, i_{21}, j_{21}, k_{21}, l_{21}, m_{21}
  226. TJug4(I_4, I_2) → U_4, V_4, b_{21}, vierhoek63, vierhoek64, p_{21}, q_{21}, r_{21}, s_{21}, t_{21}, a_{21}
  227. TJug4(K_4, A_4) → W_4, Z_4, i_{22}, vierhoek65, vierhoek66, c_{21}, d_{21}, e_{21}, f_{22}, g_{22}, h_{22}
  228. TJug4(M_4, T_1) → A_5, B_5, q_{22}, vierhoek67, vierhoek68, j_{22}, k_{22}, l_{22}, m_{22}, n_{22}, p_{22}
  229. TJug4(O_4, C_4) → C_5, D_5, d_{22}, vierhoek69, vierhoek70, r_{22}, s_{22}, t_{22}, a_{22}, b_{22}, c_{22}
  230. TJug4(Q_4, W) → E_5, F_5, k_{23}, vierhoek71, vierhoek72, e_{22}, f_{23}, g_{23}, h_{23}, i_{23}, j_{23}
  231. TAlmond14(F_3, S_4) → G_5, H_5, vierhoek73, vierhoek74, l_{23}, m_{23}, n_{23}, p_{23}, q_{23}, r_{23}
  232. TAlmond14(W_3, U_4) → I_5, J_5, vierhoek75, vierhoek76, s_{23}, t_{23}, a_{23}, b_{23}, c_{23}, d_{23}
  233. TAlmond14(W_3, I_5) → K_5, L_5, vierhoek77, vierhoek78, e_{23}, f_{24}, g_{24}, h_{24}, i_{24}, j_{24}
  234. TAlmond14(I_2, W_4) → M_5, N_5, vierhoek79, vierhoek80, k_{24}, l_{24}, m_{24}, n_{24}, p_{24}, q_{24}
  235. TAlmond14(A_4, A_5) → O_5, P_5, vierhoek81, vierhoek82, r_{24}, s_{24}, t_{24}, a_{24}, b_{24}, c_{24}
  236. TAlmond14(A_4, O_5) → Q_5, R_5, vierhoek83, vierhoek84, d_{24}, e_{24}, f_{25}, g_{25}, h_{25}, i_{25}
  237. TAlmond14(T_1, C_5) → S_5, T_5, vierhoek85, vierhoek86, j_{25}, k_{25}, l_{25}, m_{25}, n_{25}, p_{25}
  238. TAlmond14(C_4, E_5) → U_5, V_5, vierhoek87, vierhoek88, q_{25}, r_{25}, s_{25}, t_{25}, a_{25}, b_{25}
  239. TAlmond14(C_4, U_5) → W_5, Z_5, vierhoek89, vierhoek90, c_{25}, d_{25}, e_{25}, f_{26}, g_{26}, h_{26}
  240. TAlmond14(W, O) → A_6, B_6, vierhoek91, vierhoek92, i_{26}, j_{26}, k_{26}, l_{26}, m_{26}, n_{26}
  241. TAlmond14(N_3, U_3) → C_6, D_6, vierhoek93, vierhoek94, p_{26}, q_{26}, r_{26}, s_{26}, t_{26}, a_{26}
  242. TSmBiped13(D_6, U_3) → E_6, F_6, h_{27}, vierhoek95, vierhoek96, b_{26}, c_{26}, d_{26}, e_{26}, f_{27}, g_{27}
  243. TSmBiped13(H_5, S_4) → G_6, H_6, p_{27}, vierhoek97, vierhoek98, i_{27}, j_{27}, k_{27}, l_{27}, m_{27}, n_{27}
  244. TSmBiped13(L_5, I_5) → I_6, J_6, c_{27}, vierhoek99, vierhoek100, q_{27}, r_{27}, s_{27}, t_{27}, a_{27}, b_{27}
  245. TSmBiped13(J_5, U_4) → K_6, L_6, j_{28}, vierhoek101, vierhoek102, d_{27}, e_{27}, f_{28}, g_{28}, h_{28}, i_{28}
  246. TSmBiped13(N_5, W_4) → M_6, N_6, r_{28}, vierhoek103, vierhoek104, k_{28}, l_{28}, m_{28}, n_{28}, p_{28}, q_{28}
  247. TSmBiped13(R_5, O_5) → O_6, P_6, e_{28}, vierhoek105, vierhoek106, s_{28}, t_{28}, a_{28}, b_{28}, c_{28}, d_{28}
  248. TSmBiped13(P_5, A_5) → Q_6, R_6, l_{29}, vierhoek107, vierhoek108, f_{29}, g_{29}, h_{29}, i_{29}, j_{29}, k_{29}
  249. TSmBiped13(T_5, C_5) → S_6, T_6, t_{29}, vierhoek109, vierhoek110, m_{29}, n_{29}, p_{29}, q_{29}, r_{29}, s_{29}
  250. TSmBiped13(Z_5, U_5) → U_6, V_6, g_{30}, vierhoek111, vierhoek112, a_{29}, b_{29}, c_{29}, d_{29}, e_{29}, f_{30}
  251. TSmBiped13(V_5, E_5) → W_6, Z_6, n_{30}, vierhoek113, vierhoek114, h_{30}, i_{30}, j_{30}, k_{30}, l_{30}, m_{30}
  252. TSmBiped13(B_6, O) → A_7, B_7, b_{30}, vierhoek115, vierhoek116, p_{30}, q_{30}, r_{30}, s_{30}, t_{30}, a_{30}
  253. TSmBiped13(P, M) → C_7, D_7, i_{31}, vierhoek117, vierhoek118, c_{30}, d_{30}, e_{30}, f_{31}, g_{31}, h_{31}
  254. TLBiped10(I_5, L_6) → J, K, h_6, vierhoek1, vierhoek2, n_5, s_5, t_5, d_5, f_6, g_6
  255. TLBiped10(O_5, R_6) → L, E_7, k_{31}, vierhoek119, vierhoek120, i_6, j_6, k_6, l_6, m_6, j_{31}
  256. TLBiped10(U_5, Z_6) → F_7, G_7, s_{31}, vierhoek121, vierhoek122, l_{31}, m_{31}, n_{31}, p_{31}, q_{31}, r_{31}
  257. Left1(H) → H_7
  258. THRhombus6(Z_6, H_7) → I_7, driehoek1, driehoek2, t_{31}, a_{31}, b_{31}, c_{31}, d_{31}, e_{31}
  259. Right1(G) → J_7
  260. Right1(J_7) → K_7
  261. THRhombus6(K_7, F_6) → L_7, driehoek23, driehoek24, f_{32}, g_{32}, h_{32}, i_{32}, j_{32}, k_{32}
  262. TJug4(J, L_6) → M_7, N_7, s_{32}, vierhoek123, vierhoek124, l_{32}, m_{32}, n_{32}, p_{32}, q_{32}, r_{32}
  263. TJug4(L, R_6) → O_7, P_7, f_{33}, vierhoek125, vierhoek126, t_{32}, a_{32}, b_{32}, c_{32}, d_{32}, e_{32}
  264. TJug4(F_7, Z_6) → Q_7, R_7, m_{33}, vierhoek127, vierhoek128, g_{33}, h_{33}, i_{33}, j_{33}, k_{33}, l_{33}
  265. TAlmond14(Z_6, H) → S_7, T_7, vierhoek129, vierhoek130, n_{33}, p_{33}, q_{33}, r_{33}, s_{33}, t_{33}
  266. TAlmond14(R_6, I) → U_7, V_7, vierhoek131, vierhoek132, a_{33}, b_{33}, c_{33}, d_{33}, e_{33}, f_{34}
  267. TAlmond14(L_6, O_7) → W_7, Z_7, vierhoek133, vierhoek134, g_{34}, h_{34}, i_{34}, j_{34}, k_{34}, l_{34}
  268. TAlmond14(F_6, M_7) → A_8, B_8, vierhoek135, vierhoek136, m_{34}, n_{34}, p_{34}, q_{34}, r_{34}, s_{34}
  269. TSmBiped13(T_7, H) → C_8, D_8, f_{35}, vierhoek137, vierhoek138, t_{34}, a_{34}, b_{34}, c_{34}, d_{34}, e_{34}
  270. TSmBiped13(V_7, I) → E_8, F_8, m_{35}, vierhoek139, vierhoek140, g_{35}, h_{35}, i_{35}, j_{35}, k_{35}, l_{35}
  271. TSmBiped13(Z_7, O_7) → G_8, H_8, a_{35}, vierhoek141, vierhoek142, n_{35}, p_{35}, q_{35}, r_{35}, s_{35}, t_{35}
  272. TSmBiped13(B_8, M_7) → I_8, J_8, h_{36}, vierhoek143, vierhoek144, b_{35}, c_{35}, d_{35}, e_{35}, f_{36}, g_{36}
  273. Segment(N_3, C_6) → f_3
  274. EAlmond3(F_1, E_1, J_1) → K_8, L_8, M_8, vierhoek145, vierhoek146, driehoek25, driehoek26
  275. EAlmond3(J_1, I_1, S) → N_8, O_8, P_8, vierhoek147, vierhoek148, driehoek27, driehoek28
  276. EAlmond3(Z_1, W_1, R_1) → Q_8, R_8, S_8, vierhoek149, vierhoek150, driehoek29, driehoek30
  277. EAlmond3(R_1, Q_1, N_1) → T_8, U_8, V_8, vierhoek151, vierhoek152, driehoek31, driehoek32
  278. EAlmond3(M_2, L_2, D_2) → W_8, Z_8, A_9, vierhoek153, vierhoek154, driehoek33, driehoek34
  279. EAlmond3(R_2, Q_2, M_2) → B_9, C_9, D_9, vierhoek155, vierhoek156, driehoek35, driehoek36
  280. EAlmond3(D_3, C_3, Z_2) → E_9, F_9, G_9, vierhoek157, vierhoek158, driehoek37, driehoek38
  281. EAlmond3(J_3, I_3, D_3) → H_9, I_9, J_9, vierhoek159, vierhoek160, driehoek39, driehoek40
  282. EHSquare5(S, R) → K_9, L_9, M_9, vierhoek161, driehoek41
  283. EHSquare5(N_1, A_1) → N_9, O_9, P_9, vierhoek162, driehoek42
  284. EHSquare5(L_3, J_3) → Q_9, R_9, S_9, vierhoek163, driehoek43
  285. EHSquare5(A_1, F_1) → T_9, U_9, V_9, vierhoek164, driehoek44
  286. EHSquare5(B_2, Z_1) → W_9, Z_9, A_{10}, vierhoek165, driehoek45
  287. EHSquare5(D_2, B_2) → B_{10}, C_{10}, D_{10}, vierhoek166, driehoek46
  288. EHSquare5(Z_2, T_2) → E_{10}, F_{10}, G_{10}, vierhoek167, driehoek47
  289. EHSquare5(T_2, R_2) → H_{10}, I_{10}, J_{10}, vierhoek168, driehoek48
  290. ELBiped10(G_{10}, M_{10}, J_{10}) → N_{10}, driehoek49, driehoek50
  291. ELBiped10(D_{10}, L_{10}, A_{10}) → O_{10}, driehoek51, driehoek52
  292. ELBiped10(P_9, K_{10}, V_9) → P_{10}, driehoek53, driehoek54
  293. Polygon(M_9, Q_{10}, L_9) → driehoek55, i_{36}, j_{36}, k_{36}
  294. Polygon(M_9, S_{10}, N_8) → driehoek56, l_{36}, m_{36}, n_{36}
  295. Polygon(S_{10}, V_9, N_8) → driehoek57, p_{36}, q_{36}, v_9
  296. Polygon(T_8, T_{10}, P_9) → driehoek58, r_{36}, s_{36}, t_{36}
  297. Polygon(T_8, A_{10}, T_{10}) → driehoek59, a_{36}, b_{36}, c_{36}
  298. Polygon(C_9, U_{10}, D_{10}) → driehoek60, d_{36}, e_{36}, u_{10}
  299. Polygon(C_9, J_{10}, U_{10}) → driehoek61, f_{37}, g_{37}, h_{37}
  300. Polygon(Q_9, R_{10}, S_9) → driehoek62, i_{37}, j_{37}, k_{37}
  301. Polygon(S_9, V_{10}, I_9) → driehoek63, l_{37}, m_{37}, v_{10}
  302. Polygon(V_{10}, G_{10}, I_9) → driehoek64, n_{37}, p_{37}, q_{37}
  303. EJug4(D_{10}, O_{10}, A_{10}) → W_{10}, Z_{10}, A_{11}, vierhoek169, vierhoek170, driehoek65, driehoek66
  304. ERhombus2(A_{10}, T_{10}, P_9) → B_{11}, C_{11}, D_{11}, vierhoek171, vierhoek172, driehoek67, driehoek68
  305. ERhombus2(D_{10}, U_{10}, J_{10}) → E_{11}, F_{11}, G_{11}, vierhoek173, vierhoek174, driehoek69, driehoek70
  306. EJug4(G_{10}, N_{10}, J_{10}) → H_{11}, I_{11}, J_{11}, vierhoek175, vierhoek176, driehoek71, driehoek72
  307. EJug4(P_9, P_{10}, V_9) → K_{11}, L_{11}, M_{11}, vierhoek177, vierhoek178, driehoek73, driehoek74
  308. ERhombus2(V_9, S_{10}, M_9) → N_{11}, O_{11}, P_{11}, vierhoek179, vierhoek180, driehoek75, driehoek76
  309. ERhombus2(S_9, V_{10}, G_{10}) → Q_{11}, R_{11}, S_{11}, vierhoek181, vierhoek182, driehoek77, driehoek78
  310. EHRhombus6(M_9, Q_{10}) → T_{11}, U_{11}, V_{11}, vierhoek183, driehoek79
  311. EHRhombus6(R_{10}, S_9) → W_{11}, Z_{11}, A_{12}, vierhoek184, driehoek80
  312. ELBiped10(A_{12}, I_{12}, R_{11}) → J_{12}, driehoek81, driehoek82
  313. ELBiped10(R_{11}, H_{12}, J_{11}) → K_{12}, driehoek83, driehoek84
  314. ELBiped10(J_{11}, G_{12}, F_{11}) → L_{12}, driehoek85, driehoek86
  315. ELBiped10(F_{11}, F_{12}, A_{11}) → M_{12}, driehoek87, driehoek88
  316. ELBiped10(A_{11}, E_{12}, C_{11}) → N_{12}, driehoek89, driehoek90
  317. ELBiped10(C_{11}, D_{12}, M_{11}) → O_{12}, driehoek91, driehoek92
  318. ELBiped10(M_{11}, C_{12}, O_{11}) → P_{12}, driehoek93, driehoek94
  319. ELBiped10(O_{11}, B_{12}, V_{11}) → Q_{12}, driehoek95, driehoek96
  320. EJug4(A_{12}, J_{12}, R_{11}) → R_{12}, S_{12}, T_{12}, vierhoek185, vierhoek186, driehoek97, driehoek98
  321. EJug4(R_{11}, K_{12}, J_{11}) → U_{12}, V_{12}, W_{12}, vierhoek187, vierhoek188, driehoek99, driehoek100
  322. EJug4(J_{11}, L_{12}, F_{11}) → Z_{12}, A_{13}, B_{13}, vierhoek189, vierhoek190, driehoek101, driehoek102
  323. EJug4(F_{11}, M_{12}, A_{11}) → C_{13}, D_{13}, E_{13}, vierhoek191, vierhoek192, driehoek103, driehoek104
  324. EJug4(A_{11}, N_{12}, C_{11}) → F_{13}, G_{13}, H_{13}, vierhoek193, vierhoek194, driehoek105, driehoek106
  325. EJug4(C_{11}, O_{12}, M_{11}) → I_{13}, J_{13}, K_{13}, vierhoek195, vierhoek196, driehoek107, driehoek108
  326. EJug4(M_{11}, P_{12}, O_{11}) → L_{13}, M_{13}, N_{13}, vierhoek197, vierhoek198, driehoek109, driehoek110
  327. EJug4(O_{11}, Q_{12}, V_{11}) → O_{13}, P_{13}, Q_{13}, vierhoek199, vierhoek200, driehoek111, driehoek112
  328. EAlmond14(B_{14}, C_{14}, T_{12}) → E_{14}, driehoek113, driehoek114
  329. EAlmond14(T_{12}, Z_{13}, W_{12}) → F_{14}, driehoek115, driehoek116
  330. EAlmond14(W_{12}, W_{13}, G_{14}) → J_{14}, driehoek117, driehoek118
  331. EAlmond14(G_{14}, W_{13}, B_{13}) → K_{14}, driehoek119, driehoek120
  332. EAlmond14(B_{13}, V_{13}, E_{13}) → L_{14}, driehoek121, driehoek122
  333. EAlmond14(E_{13}, U_{13}, H_{14}) → M_{14}, driehoek123, driehoek124
  334. EAlmond14(H_{14}, U_{13}, H_{13}) → N_{14}, driehoek125, driehoek126
  335. EAlmond14(H_{13}, T_{13}, K_{13}) → O_{14}, driehoek127, driehoek128
  336. EAlmond14(K_{13}, S_{13}, I_{14}) → P_{14}, driehoek129, driehoek130
  337. EAlmond14(I_{14}, S_{13}, N_{13}) → Q_{14}, driehoek131, driehoek132
  338. EAlmond14(N_{13}, R_{13}, Q_{13}) → R_{14}, driehoek133, driehoek134
  339. EAlmond14(Q_{13}, D_{14}, A_{14}) → S_{14}, driehoek135, driehoek136
  340. ESmBiped13(H_{14}, N_{14}, H_{13}) → T_{14}, U_{14}, V_{14}, vierhoek201, vierhoek202, driehoek137, driehoek138
  341. ESmBiped13(H_{13}, O_{14}, K_{13}) → W_{14}, Z_{14}, A_{15}, vierhoek203, vierhoek204, driehoek139, driehoek140
  342. ESmBiped13(K_{13}, P_{14}, I_{14}) → B_{15}, C_{15}, D_{15}, vierhoek205, vierhoek206, driehoek141, driehoek142
  343. ESmBiped13(I_{14}, Q_{14}, N_{13}) → E_{15}, F_{15}, G_{15}, vierhoek207, vierhoek208, driehoek143, driehoek144
  344. ESmBiped13(N_{13}, R_{14}, Q_{13}) → H_{15}, I_{15}, J_{15}, vierhoek209, vierhoek210, driehoek145, driehoek146
  345. ESmBiped13(Q_{13}, S_{14}, A_{14}) → K_{15}, L_{15}, M_{15}, vierhoek211, vierhoek212, driehoek147, driehoek148
  346. ESmBiped13(E_{13}, M_{14}, H_{14}) → N_{15}, O_{15}, P_{15}, vierhoek213, vierhoek214, driehoek149, driehoek150
  347. ESmBiped13(B_{13}, L_{14}, E_{13}) → Q_{15}, R_{15}, S_{15}, vierhoek215, vierhoek216, driehoek151, driehoek152
  348. ESmBiped13(G_{14}, K_{14}, B_{13}) → T_{15}, U_{15}, V_{15}, vierhoek217, vierhoek218, driehoek153, driehoek154
  349. ESmBiped13(W_{12}, J_{14}, G_{14}) → W_{15}, Z_{15}, A_{16}, vierhoek219, vierhoek220, driehoek155, driehoek156
  350. ESmBiped13(T_{12}, F_{14}, W_{12}) → B_{16}, C_{16}, D_{16}, vierhoek221, vierhoek222, driehoek157, driehoek158
  351. ESmBiped13(B_{14}, E_{14}, T_{12}) → E_{16}, F_{16}, G_{16}, vierhoek223, vierhoek224, driehoek159, driehoek160
  352. ELBiped10(G_{16}, J_{16}, V_{15}) → K_{16}, driehoek161, driehoek162
  353. ELBiped10(V_{15}, I_{16}, D_{15}) → L_{16}, driehoek163, driehoek164
  354. ELBiped10(D_{15}, H_{16}, M_{15}) → M_{16}, driehoek165, driehoek166
  355. EJug4(G_{16}, K_{16}, V_{15}) → N_{16}, O_{16}, P_{16}, vierhoek225, vierhoek226, driehoek167, driehoek168
  356. EJug4(V_{15}, L_{16}, D_{15}) → Q_{16}, R_{16}, S_{16}, vierhoek227, vierhoek228, driehoek169, driehoek170
  357. EJug4(D_{15}, M_{16}, M_{15}) → T_{16}, U_{16}, V_{16}, vierhoek229, vierhoek230, driehoek171, driehoek172
  358. EHRhombus6(M_{15}, W_{16}) → A_{17}, B_{17}, C_{17}, vierhoek231, driehoek173
  359. EHRhombus6(Z_{16}, G_{16}) → D_{17}, E_{17}, F_{17}, vierhoek232, driehoek174
  360. Polygon(E_{16}, Z_{16}, G_{16}) → driehoek175, r_{37}, s_{37}, z_{16}
  361. Polygon(L_{15}, M_{15}, W_{16}) → driehoek176, w_{16}, t_{37}, a_{37}
  362. EAlmond14(F_{17}, H_{17}, P_{16}) → K_{17}, driehoek177, driehoek178
  363. EAlmond14(P_{16}, J_{17}, S_{16}) → L_{17}, driehoek179, driehoek180
  364. EAlmond14(S_{16}, I_{17}, V_{16}) → M_{17}, driehoek181, driehoek182
  365. EAlmond14(V_{16}, G_{17}, C_{17}) → N_{17}, driehoek183, driehoek184
  366. ESmBiped13(F_{17}, K_{17}, P_{16}) → O_{17}, P_{17}, Q_{17}, vierhoek233, vierhoek234, driehoek185, driehoek186
  367. ESmBiped13(V_{16}, N_{17}, C_{17}) → R_{17}, S_{17}, T_{17}, vierhoek235, vierhoek236, driehoek187, driehoek188
  368. ESmBiped13(P_{16}, L_{17}, S_{16}) → U_{17}, V_{17}, W_{17}, vierhoek237, vierhoek238, driehoek189, driehoek190
  369. ESmBiped13(S_{16}, M_{17}, V_{16}) → Z_{17}, A_{18}, B_{18}, vierhoek239, vierhoek240, driehoek191, driehoek192
  370. If(toon_{max}, "3D only", "layer = " + toon_{lagen}) → toon_{lagen-tekst}

AI Drawing Prompt Reference

This is a Muqarnas-style Bursa decorative pattern composed of repeating geometric units. First, key connection points are determined through rotation and intersection operations, forming basic shapes. Then, scaling transformations are applied to enlarge or shrink these shapes, creating nested structures. Finally, these shapes are combined into polygonal regions to form the complex pattern. The pattern includes squares, rhombuses, almond shapes, and bipeds, connected precisely via rotation, intersection, and scaling rules, presenting a symmetric and repetitive decorative effect.
The prompt above was compiled from the original drawing commands and is for reference only.