Escher-Inspired Patterns

GeoGebra Commands & Parameters

1. creatingpattern(B', H_4) → I_4, J_4, S_4, S_7, T_7, U_7, V_7, W_7, Z_7, A_8, B_8, C_8, D_8, T_4, E_8, F_8, G_8, H_8, I_8, J_8, K_8, L_8, q3, q4, a_2, q_3, r_3, s_3, t_3, a_3, K_4, c_3, e_3, g_4, h_4, i_4, j_4, l_4, m_4, p_4, q_4, L_4, U_4, V_4, W_4, Z_4, A_5, B_5, C_5, D_5, E_5, F_5, M_4, G_5, H_5, I_5, J_5, K_5, L_5, M_5, N_5, O_5, P_5, N_4, Q_5, R_5, S_5, T_5, U_5, V_5, W_5, Z_5, A_6, B_6, O_4, C_6, D_6, E_6, F_6, G_6, H_6, I_6, J_6, K_6, L_6, P_4, M_6, N_6, O_6, P_6, Q_6, R_6, S_6, T_6, U_6, V_6, Q_4, W_6, Z_6, A_7, B_7, C_7, D_7, E_7, F_7, G_7, H_7, R_4, I_7, J_7, K_7, L_7, M_7, N_7, O_7, P_7, Q_7, R_7
2. Midpoint(F_7, Z_6) → A_{17}
3. Midpoint(J_8, G_8) → S_{12}
4. Polygon(B, B_{17}, 4) → poly2, j, k, l, m, E, F
5. Polygon(B, B_{17}, 4) → poly1, f, g, h, i, C, D
6. Circle(B, (15 * f / 16)) → t
7. Intersect(t, m, 1) → V
8. OrthogonalLine(V, g) → n_3
9. Circle(B, (13 * f / 16)) → s
10. Intersect(s, m, 1) → U
11. Midpoint(V, U) → H_2
12. OrthogonalLine(U, g) → a
13. Circle(B, (11 * f / 16)) → r
14. Intersect(r, j) → N,
15. OrthogonalLine(N, f) → q_1
16. Circle(B, (5 * f / 16)) → e
17. Intersect(e, m, 1) → Q
18. OrthogonalLine(Q, g) → h_1
19. Intersect(h_1, q_1) → D_1
20. Intersect(e, j) → K,
21. OrthogonalLine(K, f) → m_1
22. Intersect(m_1, h) → N_1
23. Intersect(h_1, m_1) → B_1
24. Circle(B, (3 * f / 16)) → d
25. Intersect(d, j) → J,
26. OrthogonalLine(J, f) → l_1
27. Intersect(n_3, l_1) → M_2
28. Intersect(a, l_1) → W
29. Midpoint(M_2, W) → M_8
30. Intersect(d, m) → G,
31. OrthogonalLine(G, g) → i_1
32. Intersect(i_1, q_1) → C_1
33. Intersect(i_1, l_1) → Z
34. Circle(B, f / 16) → c
35. Circle(B, (7 * f / 16)) → p
36. Circle(B, (9 * f / 16)) → q
37. Intersect(c, m) → H,
38. Intersect(c, j) → I,
39. Intersect(p, j) → L,
40. Intersect(q, j) → M,
41. Intersect(s, j) → O,
42. Intersect(t, j) → P,
43. Intersect(p, m, 1) → R
44. Intersect(q, m, 1) → S
45. Intersect(r, m, 1) → T
46. OrthogonalLine(T, g) → b
47. OrthogonalLine(S, g) → f_1
48. OrthogonalLine(R, g) → g_1
49. OrthogonalLine(H, g) → j_1
50. OrthogonalLine(I, f) → k_1
51. OrthogonalLine(L, f) → n_1
52. OrthogonalLine(M, f) → p_1
53. OrthogonalLine(O, f) → r_1
54. OrthogonalLine(P, f) → s_1
55. Intersect(j_1, l_1) → A_1
56. Intersect(h_1, r_1) → E_1
57. Intersect(i_1, r_1) → F_1
58. Intersect(j_1, r_1) → G_1
59. Intersect(j_1, s_1) → H_1
60. Intersect(q_1, g_1) → I_1
61. Intersect(f_1, r_1) → J_1
62. Intersect(f_1, p_1) → K_1
63. Intersect(g_1, n_1) → L_1
64. Intersect(h_1, s_1) → M_1
65. Intersect(i_1, s_1) → O_1
66. Intersect(a, g) → P_1
67. Intersect(a, n_1) → Q_1
68. Intersect(b, p_1) → R_1
69. Intersect(b, s_1) → S_1
70. Intersect(q_1, j_1) → T_1
71. Intersect(k_1, h) → U_1
72. Intersect(n_1, h) → V_1
73. Intersect(p_1, h) → W_1
74. Intersect(q_1, h) → A_2
75. Intersect(r_1, h) → B_2
76. Intersect(s_1, h) → E_2
77. Intersect(n_3, g) → Z_1
78. Intersect(l_1, h) → C_2
79. Intersect(b, g) → D_2
80. Intersect(f_1, g) → F_2
81. Intersect(g_1, g) → G_2
82. Intersect(h_1, g) → I_2
83. Intersect(i_1, g) → J_2
84. Intersect(j_1, g) → K_2
85. Intersect(n_3, k_1) → L_2
86. Intersect(n_3, m_1) → N_2
87. Intersect(n_3, n_1) → O_2
88. Intersect(n_3, p_1) → P_2
89. Intersect(n_3, q_1) → Q_2
90. Intersect(n_3, r_1) → R_2
91. Intersect(n_3, s_1) → S_2
92. Intersect(a, s_1) → T_2
93. Intersect(a, r_1) → U_2
94. Intersect(a, q_1) → V_2
95. Intersect(a, p_1) → W_2
96. Intersect(a, m_1) → Z_2
97. Intersect(a, k_1) → A_3
98. Intersect(b, k_1) → B_3
99. Intersect(b, l_1) → C_3
100. Intersect(b, m_1) → D_3
101. Intersect(b, n_1) → E_3
102. Intersect(b, q_1) → F_3
103. Intersect(b, r_1) → G_3
104. Intersect(f_1, s_1) → H_3
105. Intersect(f_1, q_1) → I_3
106. Intersect(n_1, f_1) → J_3
107. Intersect(f_1, m_1) → K_3
108. Intersect(f_1, l_1) → L_3
109. Intersect(f_1, k_1) → M_3
110. Intersect(g_1, k_1) → N_3
111. Intersect(g_1, l_1) → O_3
112. Intersect(g_1, m_1) → P_3
113. Intersect(g_1, p_1) → Q_3
114. Intersect(g_1, r_1) → R_3
115. Intersect(g_1, s_1) → S_3
116. Intersect(h_1, p_1) → T_3
117. Intersect(h_1, n_1) → U_3
118. Intersect(h_1, l_1) → V_3
119. Intersect(h_1, k_1) → W_3
120. Intersect(i_1, k_1) → Z_3
121. Intersect(i_1, m_1) → A_4
122. Intersect(i_1, n_1) → B_4
123. Intersect(i_1, p_1) → C_4
124. Intersect(p_1, j_1) → D_4
125. Intersect(j_1, n_1) → E_4
126. Intersect(j_1, m_1) → F_4
127. Intersect(k_1, j_1) → G_4
128. Segment(V, Z_1) → t_1
129. Segment(U, P_1) → a_1
130. Segment(T, D_2) → b_1
131. Segment(S, F_2) → c_1
132. Segment(R, G_2) → d_1
133. Segment(Q, I_2) → e_1
134. Segment(G, J_2) → f_2
135. Segment(H, K_2) → g_2
136. Segment(U_1, I) → h_2
137. Segment(J, C_2) → i_2
138. Segment(N_1, K) → j_2
139. Segment(L, V_1) → k_2
140. Segment(W_1, M) → l_2
141. Segment(N, A_2) → m_2
142. Segment(B_2, O) → n_2
143. Segment(E_2, P) → p_2
144. Polygon(H_2, M_8, Z, C_1, D_1, B_1, N_1, D) → poly3, b_2, c_2, d_2, d_3, n_4, r_7, s_7, t_7
145. Polygon(J, A_1, H_1, P) → q1, k_3, b_3, f_4, k_4
146. Polygon(E_1, F_1, O_1, M_1) → q2, e_2, f_3, o_1, m_3
147. Polygon(I_4, S_{12}, A_{17}, V_6, D_5, F_5, Z_4, N_4) → poly5, f_5, i_5, n_5, d_5, b_7, c_7, d_7, f_8
148. Polygon(T_1, G_1, L_1, I_1, J_1, K_1, R_1, S_1, P, B_{17}, P_1, Q_1) → poly4, q_2, p_3, k_5, k_6, r_2, s_2, t_2, g_3, h_3, i_3, j_3, l_3
149. Polygon(J_5, M_5, A_7, E_7) → q5, j_5, m_5, a_7, e_7
150. Polygon(E_6, U_4, W_5, K_7) → q6, h_5, e_6, h_7, i_7
151. Polygon(D_8, R_5, N_6, B_6, F_6, J_6, S_7, W_7, K_7, H_4, L_7, O_7) → poly6, r_5, n_7, p_7, q_7, f_6, j_6, n_6, b_6, j_7, k_7, l_7, m_7
152. creatingpattern(A, N_8) → O_8, P_8, A_9, A_{12}, B_{12}, C_{12}, D_{12}, E_{12}, F_{12}, G_{12}, H_{12}, I_{12}, J_{12}, B_9, K_{12}, L_{12}, M_{12}, N_{12}, O_{12}, P_{12}, Q_{12}, R_{12}, q7, q8, r_4, s_4, t_4, a_4, b_4, c_4, Q_8, d_4, e_4, g_5, l_5, p_5, q_5, s_5, t_5, a_5, b_5, R_8, C_9, D_9, E_9, F_9, G_9, H_9, I_9, J_9, K_9, L_9, S_8, M_9, N_9, O_9, P_9, Q_9, R_9, S_9, T_9, U_9, V_9, T_8, W_9, Z_9, A_{10}, B_{10}, C_{10}, D_{10}, E_{10}, F_{10}, G_{10}, H_{10}, U_8, I_{10}, J_{10}, K_{10}, L_{10}, M_{10}, N_{10}, O_{10}, P_{10}, Q_{10}, R_{10}, V_8, S_{10}, T_{10}, U_{10}, V_{10}, W_{10}, Z_{10}, A_{11}, B_{11}, C_{11}, D_{11}, W_8, E_{11}, F_{11}, G_{11}, H_{11}, I_{11}, J_{11}, K_{11}, L_{11}, M_{11}, N_{11}, Z_8, O_{11}, P_{11}, Q_{11}, R_{11}, S_{11}, T_{11}, U_{11}, V_{11}, W_{11}, Z_{11}
153. Polygon(A_9, F_{12}, U_{10}, C_{11}, L_9, J_9, W_9, O_8) → poly7, a_9, f_{12}, u_{10}, c_{11}, l_9, j_9, w_9, o_8
154. Polygon(P_9, S_9, G_{11}, K_{11}) → q9, p_9, s_9, g_{11}, k_{11}
155. Polygon(K_{10}, C_9, E_{10}, Q_{11}) → q10, k_{10}, c_9, e_{10}, q_{11}
156. Polygon(Q_{11}, N_8, I_{11}, H_{10}, J_{12}, Z_9, L_{10}, R_{10}, N_9, E_{12}, R_{11}, B_{11}, O_{11}, L_{11}, F_{11}, D_9, G_9, I_9) → poly8, q_6, i_9, i_{11}, h_{10}, j_{12}, z_9, l_{10}, r_{10}, n_9, e_{12}, n_8, r_{11}, b_{11}, o_{11}, l_{11}, f_{11}, d_9, g_9
157. creatingpattern(A', T_{12}) → U_{12}, V_{12}, G_{13}, G_{16}, H_{16}, I_{16}, J_{16}, K_{16}, L_{16}, M_{16}, N_{16}, O_{16}, P_{16}, H_{13}, Q_{16}, R_{16}, S_{16}, T_{16}, U_{16}, V_{16}, W_{16}, Z_{16}, q11, q12, c_5, e_5, g_6, h_6, i_6, l_6, W_{12}, m_6, p_6, r_6, s_6, t_6, a_6, c_6, d_6, f_7, g_7, Z_{12}, I_{13}, J_{13}, K_{13}, L_{13}, M_{13}, N_{13}, O_{13}, P_{13}, Q_{13}, R_{13}, A_{13}, S_{13}, T_{13}, U_{13}, V_{13}, W_{13}, Z_{13}, A_{14}, B_{14}, C_{14}, D_{14}, B_{13}, E_{14}, F_{14}, G_{14}, H_{14}, I_{14}, J_{14}, K_{14}, L_{14}, M_{14}, N_{14}, C_{13}, O_{14}, P_{14}, Q_{14}, R_{14}, S_{14}, T_{14}, U_{14}, V_{14}, W_{14}, Z_{14}, D_{13}, A_{15}, B_{15}, C_{15}, D_{15}, E_{15}, F_{15}, G_{15}, H_{15}, I_{15}, J_{15}, E_{13}, K_{15}, L_{15}, M_{15}, N_{15}, O_{15}, P_{15}, Q_{15}, R_{15}, S_{15}, T_{15}, F_{13}, U_{15}, V_{15}, W_{15}, Z_{15}, A_{16}, B_{16}, C_{16}, D_{16}, E_{16}, F_{16}
158. Polygon(G_{13}, L_{16}, C_{15}, I_{15}, R_{13}, P_{13}, E_{14}, U_{12}) → poly9, g_{13}, l_{16}, c_{15}, i_{15}, r_{13}, p_{13}, e_{14}, u_{12}
159. Polygon(R_{15}, L_{15}, Z_{14}, T_{13}, K_{16}, W_{15}, T_{12}, Z_{15}, H_{15}, U_{15}, J_{13}, M_{13}, O_{13}, O_{15}, N_{14}, P_{16}, F_{14}, R_{14}) → poly10, r_{15}, r_{14}, z_{14}, t_{13}, k_{16}, w_{15}, t_{12}, z_{15}, h_{15}, u_{15}, l_{15}, j_{13}, m_{13}, o_{13}, o_{15}, n_{14}, p_{16}, f_{14}
160. Polygon(V_{13}, A_{14}, M_{15}, Q_{15}) → q13, v_{13}, a_{14}, m_{15}, q_{15}
161. Polygon(I_{13}, Q_{14}, W_{15}, K_{14}) → q14, i_{13}, q_{14}, w_1, k_{14}
162. LaTeX(button1, true, true) → text1