Pythagorean Tessellation Demo
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This example demonstrates a stochastic fractal tiling based on the Pythagorean theorem, iteratively constructing right triangles of varying side lengths to fill a plane. It involves core mathematical concepts like the Pythagorean theorem, stochastic processes, statistics, step functions, and tangent lines. The construction uses commands such as Line, OrthogonalLine, Point, Segment, Intersect, and Polygon. Suitable for high school and above, it illustrates the integration of fractal geometry, random processes, and geometric constructions.
GeoGebra Commands & Parameters
Line(A, B) → aOrthogonalLine(A, a) → bOrthogonalLine(B, a) → cPoint(b) → COrthogonalLine(C, b) → dPoint(a) → DOrthogonalLine(D, a) → ePoint(a) → EOrthogonalLine(E, a) → fPoint(a) → FOrthogonalLine(F, a) → gPoint(a) → GOrthogonalLine(G, a) → hPoint(a) → HOrthogonalLine(H, a) → iPoint(e) → IOrthogonalLine(I, e) → jPoint(e) → JOrthogonalLine(J, e) → kPoint(g) → KOrthogonalLine(K, g) → lPoint(c) → LOrthogonalLine(L, c) → mPoint(g) → MOrthogonalLine(M, g) → nPoint(a) → NSegment(N, O) → pSegment(O, P) → qSegment(B, Q) → rPoint(e) → RSegment(Q, R) → sIntersect(d, e) → SSegment(S, T) → tPoint(c) → USegment(T, U) → a_1Segment(D, V) → b_1Point(d) → WSegment(V, W) → c_1Segment(A, Z) → d_1Segment(Z, U) → e_1Segment(A_1, P) → f_1Point(b) → B_1Segment(A_1, B_1) → g_1Segment(C, C_1) → h_1Point(a) → D_1Segment(C_1, D_1) → i_1Segment(B, E_1) → j_1Point(d) → F_1Segment(E_1, F_1) → k_1Segment(A, G_1) → l_1Point(j) → H_1Segment(G_1, H_1) → m_1Intersect(c, j) → I_1Segment(I_1, J_1) → n_1Segment(J_1, D_1) → p_1Segment(B, K_1) → q_1Point(b) → L_1Segment(K_1, L_1) → r_1Intersect(b, j) → M_1Segment(M_1, N_1) → s_1Point(c) → O_1Segment(N_1, O_1) → t_1Segment(B, P_1) → a_2Point(j) → Q_1Segment(P_1, Q_1) → b_2Segment(D, R_1) → c_2Segment(R_1, O_1) → d_2Segment(I, S_1) → e_2Segment(S_1, N) → f_2Segment(I_1, T_1) → g_2Point(e) → U_1Segment(T_1, U_1) → h_2Segment(V_1, S) → i_2Point(a) → W_1Segment(V_1, W_1) → j_2Intersect(d, f) → Z_1Segment(Z_1, A_2) → k_2Segment(A_2, R) → l_2Segment(E, B_2) → m_2Point(d) → C_2Segment(B_2, C_2) → n_2Segment(D, D_2) → p_2Point(f) → E_2Segment(D_2, E_2) → q_2Intersect(f, j) → F_2Segment(F_2, G_2) → r_2Segment(G_2, W_1) → s_2Segment(I, H_2) → t_2Point(f) → I_2Segment(H_2, I_2) → a_3Segment(D, J_2) → b_3Point(j) → K_2Segment(J_2, K_2) → c_3Segment(E, L_2) → d_3Segment(L_2, U_1) → e_3Segment(Z_1, M_2) → f_3Point(a) → N_2Segment(M_2, N_2) → g_3Segment(E, O_2) → h_3Point(g) → P_2Segment(O_2, P_2) → i_3Segment(F, Q_2) → j_3Point(d) → R_2Segment(Q_2, R_2) → k_3Intersect(d, g) → S_2Segment(S_2, T_2) → l_3Segment(T_2, E_2) → m_3Segment(U_2, E) → n_3Point(j) → V_2Segment(U_2, V_2) → p_3Segment(F_2, W_2) → q_3Point(g) → Z_2Segment(W_2, Z_2) → r_3Intersect(g, j) → A_3Segment(A_3, B_3) → s_3Segment(B_3, N_2) → t_3Segment(F, C_3) → a_4Segment(C_3, I_2) → b_4Segment(C, D_3) → c_4Point(h) → E_3Segment(D_3, E_3) → d_4Segment(A, F_3) → e_4Point(d) → G_3Segment(F_3, G_3) → f_4Intersect(d, h) → H_3Segment(H_3, I_3) → g_4Point(a) → J_3Segment(J_3, I_3) → h_4Segment(G, K_3) → i_4Segment(K_3, B_1) → j_4Segment(G, L_3) → k_4Point(j) → M_3Segment(L_3, M_3) → l_4Segment(M_1, N_3) → m_4Segment(N_3, J_3) → n_4Segment(O_3, A) → p_4Point(h) → P_3Segment(O_3, P_3) → q_4Intersect(h, j) → Q_3Segment(Q_3, R_3) → r_4Segment(R_3, L_1) → s_4Segment(H_3, S_3) → t_4Point(i) → T_3Segment(S_3, T_3) → a_5Segment(G, U_3) → b_5Point(d) → V_3Segment(U_3, V_3) → c_5Segment(H, W_3) → d_5Segment(W_3, E_3) → e_5Intersect(d, i) → Z_3Segment(Z_3, A_4) → f_5Point(a) → B_4Segment(A_4, B_4) → g_5Segment(G, C_4) → h_5Point(i) → D_4Segment(C_4, D_4) → i_5Segment(H, E_4) → j_5Point(j) → F_4Segment(E_4, F_4) → k_5Intersect(i, j) → G_4Segment(G_4, H_4) → l_5Segment(H_4, P_3) → m_5Segment(Q_3, I_4) → n_5Segment(I_4, B_4) → p_5Segment(Q_3, J_4) → q_5Point(i) → K_4Segment(J_4, K_4) → r_5Segment(L_4, M_4) → s_5Segment(N_4, O_4) → t_5Segment(M_4, F_4) → a_6Intersect(i, k) → P_4Segment(P_4, Q_4) → b_6Point(h) → R_4Segment(Q_4, R_4) → c_6Segment(G_4, S_4) → d_6Point(k) → T_4Segment(S_4, T_4) → e_6Segment(M_1, U_4) → f_6Segment(U_4, R_4) → g_6Segment(V_4, W_4) → h_6Segment(W_4, M_3) → i_6Segment(Z_4, Q_3) → j_6Point(k) → A_5Segment(A_5, Z_4) → k_6Segment(B_5, M_1) → l_6Point(k) → C_5Segment(C_5, B_5) → m_6Segment(D_5, I_1) → n_6Point(b) → E_5Segment(D_5, E_5) → p_6Intersect(b, k) → F_5Segment(F_5, G_5) → q_6Point(c) → H_5Segment(G_5, H_5) → r_6Intersect(c, k) → I_5Segment(I_5, J_5) → s_6Segment(J_5, H_1) → t_6Segment(O_4, E_5) → a_7Segment(I_5, K_5) → b_7Point(e) → L_5Segment(K_5, L_5) → c_7Segment(J, M_5) → d_7Segment(M_5, Q_1) → e_7Segment(I, N_5) → f_7Segment(N_5, H_5) → g_7Segment(I_1, O_5) → h_7Point(k) → P_5Segment(O_5, P_5) → i_7Segment(F_2, Q_5) → j_7Segment(Q_5, L_5) → k_7Segment(J, R_5) → l_7Point(f) → S_5Segment(R_5, S_5) → m_7Intersect(f, k) → T_5Segment(T_5, U_5) → n_7Segment(U_5, K_2) → p_7Segment(V_5, I) → q_7Point(k) → W_5Segment(W_5, V_5) → r_7Segment(Z_5, F_2) → s_7Point(k) → A_6Segment(A_6, Z_5) → t_7Segment(S_5, B_6) → a_8Segment(B_6, M_2) → b_8Segment(A_3, B_6) → c_8Intersect(g, k) → C_6Segment(C_6, D_6) → d_8Segment(D_6, V_2) → e_8Segment(T_5, E_6) → f_8Point(g) → F_6Segment(E_6, F_6) → g_8Point(d) → G_6OrthogonalLine(G_6, d) → h_8Segment(F, H_6) → i_8Point(h_8) → I_6Segment(H_6, I_6) → j_8Intersect(a, h_8) → J_6Segment(J_6, K_6) → k_8Point(d) → L_6Segment(K_6, L_6) → l_8Segment(M_6, G_6) → m_8Segment(M_6, P_2) → n_8Segment(N_6, S_2) → p_8Segment(N_6, O_6) → q_8Segment(P_6, F) → r_8Segment(J_6, Q_6) → s_8Segment(Q_6, Z_2) → t_8Point(j) → R_6Segment(R_6, P_6) → a_9Intersect(j, h_8) → S_6Segment(S_6, T_6) → b_9Segment(T_6, O_6) → c_9Segment(A_3, U_6) → d_9Point(h_8) → V_6Segment(U_6, V_6) → e_9Segment(A_3, W_6) → f_9Point(k) → Z_6Segment(W_6, Z_6) → g_9Segment(C_6, A_7) → h_9Point(h_8) → B_7Segment(A_7, B_7) → i_9Segment(S_6, C_7) → j_9Segment(C_7, F_6) → k_9Intersect(k, h_8) → D_7Segment(D_7, E_7) → l_9Segment(E_7, R_6) → m_9Segment(F_7, P_4) → n_9Intersect(h, l) → G_7Segment(G_7, H_7) → p_9Intersect(i, l) → I_7Segment(I_7, J_7) → q_9Point(h) → K_7Segment(J_7, K_7) → r_9Segment(H_7, T_4) → s_9Point(i) → L_7Segment(L_7, N_4) → t_9Point(l) → M_7Segment(M_7, F_7) → a_{10}Segment(N_7, G_7) → b_{10}Segment(O_7, I_7) → c_{10}Intersect(i, m) → P_7Segment(P_7, Q_7) → d_{10}Intersect(h, m) → S_7Segment(R_7, S_7) → e_{10}Segment(R_7, M_7) → f_{10}Point(h) → T_7Segment(Q_7, T_7) → g_{10}Point(i) → U_7Segment(U_7, N_7) → h_{10}Point(m) → V_7Segment(V_7, O_7) → i_{10}Segment(W_7, F_5) → j_{10}Segment(W_7, K_7) → k_{10}Point(l) → Z_7Segment(Z_7, L_4) → l_{10}Segment(G_7, A_8) → m_{10}Point(b) → B_8Segment(A_8, B_8) → n_{10}Intersect(b, l) → C_8Segment(C_8, D_8) → p_{10}Segment(D_8, A_5) → q_{10}Point(l) → E_8Segment(E_8, V_4) → r_{10}Segment(I_5, F_8) → s_{10}Segment(F_8, B_8) → t_{10}Intersect(c, l) → G_8Segment(G_8, H_8) → a_{11}Segment(H_8, C_5) → b_{11}Segment(C_8, I_8) → c_{11}Point(c) → J_8Segment(I_8, J_8) → d_{11}Segment(K_8, I_5) → e_{11}Segment(L_8, G_8) → f_{11}Intersect(e, l) → M_8Segment(M_8, N_8) → g_{11}Segment(N_8, P_5) → h_{11}Point(e) → O_8Segment(L_8, O_8) → i_{11}Segment(J, P_8) → j_{11}Segment(P_8, J_8) → k_{11}Point(l) → R_8Segment(R_8, K_8) → l_{11}Segment(S_8, J) → m_{11}Segment(M_8, T_8) → n_{11}Point(f) → U_8Segment(T_8, U_8) → p_{11}Segment(V_8, T_5) → q_{11}Segment(V_8, O_8) → r_{11}Intersect(f, l) → W_8Segment(W_8, Z_8) → s_{11}Segment(Z_8, W_5) → t_{11}Point(l) → A_9Segment(A_9, S_8) → a_{12}Segment(B_9, C_6) → b_{12}Segment(C_9, T_5) → c_{12}Segment(W_8, D_9) → d_{12}Point(g) → E_9Segment(D_9, E_9) → e_{12}Point(l) → F_9Segment(F_9, C_9) → f_{12}Segment(U_8, B_9) → g_{12}Segment(K, G_9) → h_{12}Segment(G_9, A_6) → i_{12}Segment(H_9, C_6) → j_{12}Segment(D_7, I_9) → k_{12}Segment(I_9, E_9) → l_{12}Segment(K, J_9) → m_{12}Point(h_8) → K_9Segment(J_9, K_9) → n_{12}Intersect(l, h_8) → L_9Segment(L_9, M_9) → p_{12}Segment(M_9, Z_6) → q_{12}Point(l) → N_9Segment(H_9, N_9) → r_{12}Segment(O_9, G_7) → s_{12}Point(m) → P_9Segment(P_9, O_9) → t_{12}Segment(S_7, Q_9) → a_{13}Point(b) → R_9Segment(Q_9, R_9) → b_{13}Segment(S_9, C_8) → c_{13}Segment(C_8, T_9) → d_{13}Segment(T_7, S_9) → e_{13}Intersect(b, m) → U_9Segment(U_9, V_9) → f_{13}Segment(V_9, Z_7) → g_{13}Segment(W_9, G_8) → h_{13}Segment(U_9, Z_9) → i_{13}Segment(L, A_{10}) → j_{13}Segment(A_{10}, E_8) → k_{13}Point(c) → B_{10}Segment(Z_9, B_{10}) → l_{13}Segment(R_9, W_9) → m_{13}Point(m) → C_{10}Segment(C_{10}, T_9) → n_{13}Segment(D_{10}, G_8) → p_{13}Point(m) → E_{10}Segment(E_{10}, D_{10}) → q_{13}Segment(L, F_{10}) → r_{13}Point(e) → G_{10}Segment(F_{10}, G_{10}) → s_{13}Intersect(e, m) → H_{10}Segment(H_{10}, I_{10}) → t_{13}Segment(I_{10}, R_8) → a_{14}Segment(B_{10}, J_{10}) → b_{14}Segment(J_{10}, M_8) → c_{14}Segment(K_{10}, W_8) → d_{14}Segment(L_{10}, M_8) → e_{14}Segment(H_{10}, M_{10}) → f_{14}Intersect(f, m) → N_{10}Segment(N_{10}, O_{10}) → g_{14}Segment(O_{10}, A_9) → h_{14}Point(f) → P_{10}Segment(M_{10}, P_{10}) → i_{14}Point(m) → Q_{10}Segment(L_{10}, Q_{10}) → j_{14}Segment(K_{10}, G_{10}) → k_{14}Segment(R_{10}, W_8) → l_{14}Point(m) → S_{10}Segment(S_{10}, R_{10}) → m_{14}Segment(P_{10}, T_{10}) → n_{14}Segment(T_{10}, K) → p_{14}Intersect(g, m) → U_{10}Segment(U_{10}, V_{10}) → q_{14}Segment(V_{10}, F_9) → r_{14}Segment(N_{10}, W_{10}) → s_{14}Point(g) → Z_{10}Segment(W_{10}, Z_{10}) → t_{14}Segment(L_9, A_{11}) → a_{15}Segment(A_{11}, Z_{10}) → b_{15}Segment(U_{10}, B_{11}) → c_{15}Point(h_8) → C_{11}Segment(B_{11}, C_{11}) → d_{15}Intersect(m, h_8) → D_{11}Segment(D_{11}, E_{11}) → e_{15}Segment(E_{11}, N_9) → f_{15}Segment(F_{11}, K) → g_{15}Point(m) → G_{11}Segment(G_{11}, F_{11}) → h_{15}Segment(H_{11}, P_7) → i_{15}Segment(I_{11}, S_7) → j_{15}Intersect(h, n) → K_{11}Segment(J_{11}, K_{11}) → k_{15}Intersect(i, n) → L_{11}Segment(L_{11}, M_{11}) → l_{15}Point(i) → N_{11}Segment(N_{11}, I_{11}) → m_{15}Segment(J_{11}, V_7) → n_{15}Point(n) → O_{11}Segment(O_{11}, H_{11}) → p_{15}Segment(P_{11}, U_9) → q_{15}Segment(P_{11}, M_{11}) → r_{15}Point(n) → Q_{11}Segment(Q_{11}, R_{11}) → s_{15}Segment(R_{11}, S_7) → t_{15}Segment(K_{11}, S_{11}) → a_{16}Point(b) → T_{11}Segment(S_{11}, T_{11}) → b_{16}Intersect(b, n) → U_{11}Segment(U_{11}, V_{11}) → c_{16}Segment(V_{11}, P_9) → d_{16}Segment(W_{11}, U_9) → e_{16}Segment(U_{11}, Z_{11}) → f_{16}Segment(Z_{11}, A_{12}) → g_{16}Point(n) → B_{12}Segment(B_{12}, W_{11}) → h_{16}Segment(C_{12}, L) → i_{16}Segment(C_{12}, T_{11}) → j_{16}Segment(D_{12}, L) → k_{16}Point(n) → E_{12}Segment(E_{12}, D_{12}) → l_{16}Intersect(c, n) → F_{12}Intersect(c, n) → G_{12}Segment(G_{12}, H_{12}) → m_{16}Segment(H_{12}, C_{10}) → n_{16}Segment(A_{12}, H_{10}) → p_{16}Intersect(e, n) → I_{12}Segment(I_{12}, J_{12}) → q_{16}Segment(J_{12}, E_{10}) → r_{16}Segment(G_{12}, K_{12}) → s_{16}Segment(N_{10}, L_{12}) → t_{16}Segment(L_{12}, K_{12}) → a_{17}Segment(M_{12}, H_{10}) → b_{17}Segment(I_{12}, N_{12}) → c_{17}Point(f) → O_{12}Segment(N_{12}, O_{12}) → d_{17}Intersect(f, n) → P_{12}Segment(P_{12}, Q_{12}) → e_{17}Segment(Q_{12}, Q_{10}) → f_{17}Point(n) → R_{12}Segment(R_{12}, M_{12}) → g_{17}Segment(S_{12}, N_{10}) → h_{17}Point(n) → T_{12}Segment(T_{12}, S_{12}) → i_{17}Segment(U_{12}, U_{10}) → j_{17}Segment(U_{12}, O_{12}) → k_{17}Segment(M, V_{12}) → l_{17}Segment(V_{12}, S_{10}) → m_{17}Segment(P_{12}, W_{12}) → n_{17}Point(g) → Z_{12}Segment(W_{12}, Z_{12}) → p_{17}Segment(D_{11}, A_{13}) → q_{17}Segment(A_{13}, Z_{12}) → r_{17}Segment(M, B_{13}) → s_{17}Point(h_8) → C_{13}Segment(B_{13}, C_{13}) → t_{17}Intersect(n, h_8) → D_{13}Segment(D_{13}, E_{13}) → a_{18}Segment(E_{13}, G_{11}) → b_{18}Segment(F_{13}, U_{10}) → c_{18}Point(n) → G_{13}Segment(G_{13}, F_{13}) → d_{18}Segment(Z_3, G_6) → e_{18}Segment(D_{13}, G_6) → f_{18}Segment(L_{11}, D_{13}) → g_{18}Segment(L_{11}, Z_3) → h_{18}Segment(H, J_6) → i_{18}Segment(G_4, S_6) → j_{18}Segment(D_7, P_4) → k_{18}Segment(I_7, L_9) → l_{18}Segment(L_9, I_7) → m_{18}Segment(P_7, D_{11}) → n_{18}Segment(L_{11}, D_{13}) → p_{18}Segment(K_{11}, H_3) → q_{18}Segment(C, U_{11}) → r_{18}Segment(G_{12}, P) → s_{18}Segment(S, I_{12}) → t_{18}Segment(P_{12}, Z_1) → a_{19}Segment(S_2, M) → b_{19}Segment(D_{13}, G_6) → c_{19}Intersect(a_5, c_5) → H_{13}Intersect(a_5, g_5) → I_{13}Intersect(e_5, g_5) → J_{13}Intersect(c_5, e_5) → K_{13}Polygon(H_{13}, I_{13}, J_{13}, K_{13}) → poly1, h_{19}, i_{19}, j_{19}, k_{19}Intersect(d_4, f_4) → L_{13}Intersect(d_4, h_4) → M_{13}Intersect(h_4, j_4) → N_{13}Intersect(f_4, j_4) → O_{13}Polygon(L_{13}, M_{13}, N_{13}, O_{13}) → poly2, l_{19}, m_{19}, n_{19}, o_{13}Intersect(g_1, k_1) → P_{13}Intersect(g_1, i_1) → Q_{13}Intersect(e_1, i_1) → R_{13}Intersect(e_1, k_1) → S_{13}Polygon(P_{13}, Q_{13}, R_{13}, S_{13}) → poly3, p_{19}, q_{19}, r_{19}, s_{19}Intersect(a_1, c_1) → T_{13}Intersect(p, a_1) → U_{13}Intersect(p, s) → V_{13}Intersect(s, c_1) → W_{13}Polygon(T_{13}, U_{13}, V_{13}, W_{13}) → poly4, t_{19}, u_{13}, v_{13}, w_{13}Intersect(l_2, n_2) → Z_{13}Intersect(j_2, l_2) → A_{14}Intersect(j_2, q_2) → B_{14}Intersect(n_2, q_2) → C_{14}Polygon(Z_{13}, A_{14}, B_{14}, C_{14}) → poly5, z_{13}, a_{20}, b_{20}, c_{20}Intersect(k_3, m_3) → D_{14}Intersect(g_3, m_3) → E_{14}Intersect(g_3, i_3) → F_{14}Intersect(i_3, k_3) → G_{14}Polygon(D_{14}, E_{14}, F_{14}, G_{14}) → poly6, d_{19}, e_{19}, f_{19}, g_{19}Intersect(l_8, n_8) → H_{14}Intersect(n_8, q_8) → I_{14}Intersect(j_8, q_8) → J_{14}Intersect(j_8, l_8) → K_{14}Polygon(H_{14}, I_{14}, J_{14}, K_{14}) → poly7, h_{20}, i_{20}, j_{20}, k_{20}Intersect(m_5, p_5) → L_{14}Intersect(i_5, p_5) → M_{14}Intersect(i_5, k_5) → N_{14}Intersect(k_5, m_5) → O_{14}Polygon(L_{14}, M_{14}, N_{14}, O_{14}) → poly8, l_{20}, m_{20}, n_{20}, o_{14}Intersect(n_4, s_4) → P_{14}Intersect(n_4, q_4) → Q_{14}Intersect(l_4, q_4) → R_{14}Intersect(l_4, s_4) → S_{14}Polygon(P_{14}, Q_{14}, R_{14}, S_{14}) → poly9, p_{20}, q_{20}, r_{20}, s_{20}Intersect(p_1, t_1) → T_{14}Intersect(p_1, r_1) → U_{14}Intersect(m_1, r_1) → V_{14}Intersect(m_1, t_1) → W_{14}Polygon(T_{14}, U_{14}, V_{14}, W_{14}) → poly10, t_{20}, u_{14}, v_{14}, w_{14}Intersect(f_2, h_2) → Z_{14}Intersect(d_2, f_2) → A_{15}Intersect(b_2, d_2) → B_{15}Intersect(b_2, h_2) → C_{15}Polygon(Z_{14}, A_{15}, B_{15}, C_{15}) → poly11, z_{14}, a_{21}, b_{21}, c_{21}Intersect(s_2, a_3) → D_{15}Intersect(s_2, e_3) → E_{15}Intersect(c_3, e_3) → F_{15}Intersect(a_3, c_3) → G_{15}Polygon(D_{15}, E_{15}, F_{15}, G_{15}) → poly12, d_{20}, e_{20}, f_{20}, g_{20}Intersect(r_3, t_3) → H_{15}Intersect(t_3, b_4) → I_{15}Intersect(p_3, b_4) → J_{15}Intersect(p_3, r_3) → K_{15}Polygon(H_{15}, I_{15}, J_{15}, K_{15}) → poly13, h_{21}, i_{21}, j_{21}, k_{21}Intersect(c_9, e_9) → L_{15}Intersect(t_8, c_9) → M_{15}Intersect(t_8, a_9) → N_{15}Intersect(a_9, e_9) → O_{15}Polygon(L_{15}, M_{15}, N_{15}, O_{15}) → poly14, l_{21}, m_{21}, n_{21}, o_{15}Intersect(a_6, c_6) → P_{15}Intersect(r_5, a_6) → Q_{15}Intersect(r_5, e_6) → R_{15}Intersect(c_6, e_6) → S_{15}Polygon(P_{15}, Q_{15}, R_{15}, S_{15}) → poly15, p_{21}, q_{21}, r_{21}, s_{21}Intersect(i_6, a_7) → T_{15}Intersect(g_6, i_6) → U_{15}Intersect(g_6, k_6) → V_{15}Intersect(k_6, a_7) → W_{15}Polygon(T_{15}, U_{15}, V_{15}, W_{15}) → poly16, t_{21}, u_{15}, v_{15}, w_{15}Intersect(r_6, t_6) → Z_{15}Intersect(p_6, t_6) → A_{16}Intersect(m_6, p_6) → B_{16}Intersect(m_6, r_6) → C_{16}Polygon(Z_{15}, A_{16}, B_{16}, C_{16}) → poly17, z_{15}, a_{22}, b_{22}, c_{22}Intersect(c_7, e_7) → D_{16}Intersect(e_7, g_7) → E_{16}Intersect(g_7, i_7) → F_{16}Intersect(c_7, i_7) → G_{16}Polygon(D_{16}, E_{16}, F_{16}, G_{16}) → poly18, d_{21}, e_{21}, f_{21}, g_{21}Intersect(m_7, p_7) → H_{16}Intersect(k_7, p_7) → I_{16}Intersect(k_7, r_7) → J_{16}Intersect(m_7, r_7) → K_{16}Polygon(H_{16}, I_{16}, J_{16}, K_{16}) → poly19, h_{22}, i_{22}, j_{22}, k_{22}Intersect(e_8, g_8) → L_{16}Intersect(a_8, e_8) → M_{16}Intersect(t_7, a_8) → N_{16}Intersect(t_7, g_8) → O_{16}Polygon(L_{16}, M_{16}, N_{16}, O_{16}) → poly20, l_{22}, m_{22}, n_{22}, o_{16}Intersect(i_9, m_9) → P_{16}Intersect(k_9, m_9) → Q_{16}Intersect(g_9, k_9) → R_{16}Intersect(g_9, i_9) → S_{16}Polygon(P_{16}, Q_{16}, R_{16}, S_{16}) → poly21, p_{22}, q_{22}, r_{22}, s_{22}Intersect(r_9, s_9) → T_{16}Intersect(s_9, t_9) → U_{16}Intersect(t_9, a_{10}) → V_{16}Intersect(r_9, a_{10}) → W_{16}Point(r_9) → Z_{16}Polygon(U_{16}, V_{16}, W_{16}, T_{16}) → poly22, u_{16}, v_{16}, w_{16}, t_{22}Intersect(n_{10}, q_{10}) → A_{17}Intersect(k_{10}, q_{10}) → B_{17}Intersect(k_{10}, l_{10}) → C_{17}Intersect(l_{10}, n_{10}) → D_{17}Polygon(A_{17}, B_{17}, C_{17}, D_{17}) → poly23, a_{23}, b_{23}, c_{23}, d_{22}Intersect(b_{11}, d_{11}) → E_{17}Intersect(t_{10}, b_{11}) → F_{17}Intersect(r_{10}, t_{10}) → G_{17}Intersect(r_{10}, d_{11}) → H_{17}Polygon(E_{17}, F_{17}, G_{17}, H_{17}) → poly24, e_{22}, f_{22}, g_{22}, h_{23}Intersect(h_{11}, i_{11}) → I_{17}Intersect(h_{11}, k_{11}) → J_{17}Intersect(k_{11}, l_{11}) → K_{17}Intersect(i_{11}, l_{11}) → L_{17}Polygon(I_{17}, J_{17}, K_{17}, L_{17}) → poly25, i_{23}, j_{23}, k_{23}, l_{23}Intersect(p_{11}, t_{11}) → M_{17}Intersect(r_{11}, t_{11}) → N_{17}Intersect(r_{11}, a_{12}) → O_{17}Intersect(p_{11}, a_{12}) → P_{17}Polygon(M_{17}, N_{17}, O_{17}, P_{17}) → poly26, m_{23}, n_{23}, o_{17}, p_{23}Intersect(e_{12}, i_{12}) → Q_{17}Intersect(g_{12}, i_{12}) → R_{17}Intersect(f_{12}, g_{12}) → S_{17}Intersect(e_{12}, f_{12}) → T_{17}Polygon(Q_{17}, R_{17}, S_{17}, T_{17}) → poly27, q_{23}, r_{23}, s_{23}, t_{23}Intersect(l_{12}, r_{12}) → U_{17}Intersect(n_{12}, r_{12}) → V_{17}Intersect(n_{12}, q_{12}) → W_{17}Polygon(U_{17}, V_{17}, W_{17}, Z_{17}) → poly28, u_{17}, v_{17}, w_{17}, z_{17}Intersect(f_{10}, g_{10}) → B_{18}Intersect(f_{10}, h_{10}) → C_{18}Intersect(h_{10}, i_{10}) → D_{18}Intersect(g_{10}, i_{10}) → E_{18}Polygon(B_{18}, C_{18}, D_{18}, E_{18}) → poly29, b_{24}, c_{24}, d_{23}, e_{23}Intersect(b_{13}, g_{13}) → F_{18}Intersect(e_{13}, g_{13}) → G_{18}Intersect(t_{12}, e_{13}) → H_{18}Intersect(t_{12}, b_{13}) → I_{18}Polygon(F_{18}, G_{18}, H_{18}, I_{18}) → poly30, f_{23}, g_{23}, h_{24}, i_{24}Intersect(k_{13}, l_{13}) → J_{18}Intersect(k_{13}, m_{13}) → K_{18}Intersect(m_{13}, n_{13}) → L_{18}Intersect(l_{13}, n_{13}) → M_{18}Polygon(J_{18}, K_{18}, L_{18}, M_{18}) → poly31, j_{24}, k_{24}, l_{24}, m_{24}Intersect(a_{14}, b_{14}) → N_{18}Intersect(q_{13}, b_{14}) → O_{18}Intersect(q_{13}, s_{13}) → P_{18}Intersect(s_{13}, a_{14}) → Q_{18}Polygon(N_{18}, O_{18}, P_{18}, Q_{18}) → poly32, n_{24}, o_{18}, p_{24}, q_{24}Intersect(h_{14}, i_{14}) → R_{18}Point(h_{14}) → S_{18}Intersect(j_{14}, k_{14}) → T_{18}Intersect(i_{14}, j_{14}) → U_{18}Polygon(R_{18}, S_{18}, T_{18}, U_{18}) → poly33, r_{24}, s_{24}, t_{24}, u_{18}Intersect(r_{14}, t_{14}) → V_{18}Intersect(n_{14}, r_{14}) → W_{18}Intersect(m_{14}, n_{14}) → Z_{18}Intersect(m_{14}, t_{14}) → A_{19}Polygon(V_{18}, W_{18}, Z_{18}, A_{19}) → poly34, v_{18}, w_{18}, z_{18}, a_{24}Intersect(b_{15}, h_{15}) → B_{19}Intersect(d_{15}, h_{15}) → C_{19}Intersect(d_{15}, f_{15}) → D_{19}Point(f_{15}) → E_{19}Polygon(B_{19}, C_{19}, D_{19}, E_{19}) → poly35, b_{25}, c_{25}, d_{24}, e_{24}Intersect(n_{15}, r_{15}) → F_{19}Intersect(m_{15}, n_{15}) → G_{19}Intersect(m_{15}, p_{15}) → H_{19}Intersect(p_{15}, r_{15}) → I_{19}Polygon(F_{19}, G_{19}, H_{19}, I_{19}) → poly36, f_{24}, g_{24}, h_{25}, i_{25}Intersect(b_{16}, d_{16}) → J_{19}Intersect(r_{15}, d_{16}) → K_{19}Intersect(r_{15}, s_{15}) → L_{19}Intersect(s_{15}, b_{16}) → M_{19}Polygon(J_{19}, K_{19}, L_{19}, M_{19}) → poly37, j_{25}, k_{25}, l_{25}, m_{25}Intersect(g_{16}, n_{16}) → N_{19}Intersect(j_{16}, n_{16}) → O_{19}Intersect(h_{16}, j_{16}) → P_{19}Intersect(g_{16}, h_{16}) → Q_{19}Polygon(N_{19}, O_{19}, P_{19}, Q_{19}) → poly38, n_{25}, o_{19}, p_{25}, q_{25}Intersect(r_{16}, a_{17}) → R_{19}Intersect(g_{16}, r_{16}) → S_{19}Intersect(g_{16}, l_{16}) → T_{19}Intersect(l_{16}, a_{17}) → U_{19}Polygon(R_{19}, S_{19}, T_{19}, U_{19}) → poly39, r_{25}, s_{25}, t_{25}, u_{19}Intersect(a_{17}, f_{17}) → V_{19}Intersect(a_{17}, g_{17}) → W_{19}Intersect(d_{17}, g_{17}) → Z_{19}Intersect(d_{17}, f_{17}) → A_{20}Polygon(V_{19}, W_{19}, Z_{19}, A_{20}) → poly40, v_{19}, w_{19}, z_{19}, a_{25}Intersect(k_{17}, m_{17}) → B_{20}Intersect(i_{17}, k_{17}) → C_{20}Intersect(i_{17}, p_{17}) → D_{20}Intersect(m_{17}, p_{17}) → E_{20}Polygon(B_{20}, C_{20}, D_{20}, E_{20}) → poly41, b_{26}, c_{26}, d_{25}, e_{25}Intersect(r_{17}, b_{18}) → F_{20}Intersect(r_{17}, d_{18}) → G_{20}Intersect(t_{17}, d_{18}) → H_{20}Intersect(t_{17}, b_{18}) → I_{20}Polygon(F_{20}, G_{20}, H_{20}, I_{20}) → poly42, f_{25}, g_{25}, h_{26}, i_{26}Segment(B_2, J_2) → a_{26}Polygon(E, B_2, J_2, F_{15}, E_{15}, L_2) → poly43, e_{26}, b_{27}, j_{26}, f_{26}, e_{27}, l_{26}Polygon(B_2, C_{14}, D_2, D, J_2) → poly44, b_{28}, c_{27}, d_{26}, d_{27}, j_{27}Segment(A_2, O_2) → g_{26}Polygon(Z_{13}, B_2, E, O_2, A_2) → poly45, z_1, b_{29}, e_{28}, o_2, a_{27}Polygon(M_2, Z_1, A_2, O_2, F_{14}) → poly46, m_{26}, z_2, a_{28}, o_1, f_{27}Segment(Q_2, U_2) → k_{26}Segment(K_6, P_6) → n_{26}Segment(H_6, T_2) → p_{26}Segment(U_6, C_3) → q_{26}Segment(B_3, Z_5) → r_{26}Segment(A_7, B_6) → s_{26}Segment(W_6, T_6) → t_{26}Polygon(W_2, L_2, E, U_2, K_{15}) → poly47, w_2, l_{27}, e_{29}, u_2, k_{27}Polygon(W_2, L_2, E_{15}, G_2, F_2) → poly48, w_1, l_{28}, e_{30}, g_{27}, f_{28}Polygon(G_{14}, O_2, E, U_2, Q_2) → poly49, g_{28}, o_3, e_{31}, u_1, q_{27}Polygon(J_{15}, U_2, Q_2, F, C_3) → poly50, j_{28}, u_3, q_{28}, f_{29}, c_{28}Polygon(D_2, T, S, V_1, B_{14}) → poly51, d_{28}, t_{27}, s_{27}, v_1, b_{30}Polygon(C_{14}, B_2, J_2, D, D_2) → poly52, c_{29}, b_{31}, j_{29}, d_{29}, d_{30}Polygon(D_2, T, T_{13}, V, D) → poly53, d_{31}, t_{28}, t_{29}, v, d_{32}Polygon(D, R_1, H_2, G_{15}, J_2) → poly54, d_{33}, r_{27}, h_{27}, g_{29}, j_{30}Polygon(D, V, P_1, B_{15}, R_1) → poly55, d_{34}, v_2, p_{27}, b_{32}, r_{28}Polygon(U_{14}, D_1, F_3, O_{13}, N_{13}, J_3, G_1, V_{14}) → poly56, u_4, d_{35}, f_{30}, o_4, n_{27}, j_{31}, g_{30}, v_3Polygon(T_{14}, J_1, Q_1, E_{16}, F_{16}, O_5, H_1, W_{14}) → poly57, t_{30}, j_{32}, q_{29}, e_{32}, f_{31}, o_5, h_{28}, w_3Polygon(E, B_2, C_{14}, B_{14}, E_{15}, F_{15}, J_2, D, W_1) → poly58, e_{33}, b_{33}, c_{30}, b_{34}, e_{34}, f_{32}, j_{33}, d_{36}, w_4Polygon(E, L_2, E_{15}, D_{15}, J_{15}, K_{15}, W_2, F_2, I_2) → poly59, e_{35}, l_{29}, e_{36}, d_{37}, j_{34}, k_{28}, w_5, f_{33}, i_{27}Polygon(G_{15}, F_{15}, U_1, Z_{14}, A_{15}, R_1, D, I, H_2) → poly60, g_{31}, f_{34}, u_5, z_3, a_{29}, r_{29}, d_{38}, i_{28}, h_{29}Polygon(F_2, G_2, D_{15}, G_{15}, I_{16}, J_{16}, V_5, I, K_2) → poly61, f_{35}, g_{32}, d_{39}, g_{33}, i_{29}, j_{35}, v_5, i_{30}, k_{29}Polygon(B_{14}, A_{14}, W_{13}, T_{13}, T, S, R, D, D_2) → poly62, b_{35}, a_{30}, w_6, t_{31}, t_{32}, s_{28}, r_{30}, d_{40}, d_{41}Polygon(D, B, P_1, B_{15}, A_{15}, N, V_{13}, W_{13}, V) → poly63, d_{42}, b_{36}, p_{28}, b_{37}, a_{31}, n_{28}, v_4, w_7, v_6Polygon(R, W_{13}, V, J_2, F_{15}, U_1, D) → poly64, r_{31}, w_8, v_7, j_{36}, f_{36}, u_6, d_{43}Polygon(W_1, N, A_{15}, R_1, D, D_2, B_{14}) → poly65, w_9, n_{29}, a_{32}, r_{32}, d_{44}, d_{45}, b_{38}Segment(N_3, Z_4) → m_{27}Segment(J_5, V_4) → m_{28}Segment(L_4, W_4) → m_{29}Segment(S_4, I_4) → p_{29}Polygon(N_3, Z_4, V_{15}, W_4, V_4, J_5, B_5) → poly66, n_{30}, z_4, v_8, w_{10}, v_9, j_{37}, b_{39}Segment(Q, A_1) → s_{29}Segment(P_1, V) → h_{30}Segment(G_1, E_1) → k_{30}Segment(Z, D_3) → l_{30}Segment(C_1, F_1) → m_{30}Segment(D_2, T) → p_{30}Segment(O_2, A_2) → q_{30}Segment(H_6, T_2) → s_{30}Segment(F_{11}, M_9) → c_{31}Segment(J_9, B_9) → h_{31}Segment(S_8, U_5) → i_{31}Segment(D_9, V_8) → k_{31}Segment(L_{10}, Z_8) → l_{31}Segment(T_8, P_8) → m_{31}Segment(Q_5, E_6) → p_{31}Segment(C_9, D_6) → q_{31}Segment(R_{10}, G_9) → s_{31}Segment(T_{10}, B_{11}) → c_{32}Segment(W_{10}, K_{10}) → h_{32}Segment(D_{10}, N_8) → i_{32}Segment(S_{12}, V_{10}) → k_{32}Segment(F_{13}, E_{11}) → l_{32}Segment(K_8, M_5) → m_{32}Segment(G_5, U_4) → n_{32}Segment(N_3, Z_4) → n_{31}Polygon(G_5, U_4, M_1, B_5, C_{16}) → poly67, g_{34}, u_7, m_{33}, b_{40}, c_{33}Segment(J_1, B_5) → p_{32}Segment(D_5, K_5) → q_{32}Point(m_{28}) → M_{20}Segment(V_4, J_5) → s_{32}Polygon(J_5, Z_{15}, G_5, F_5, V_4) → poly68, j_{38}, z_5, g_{35}, f_{37}, v_{10}Polygon(A_{16}, D_5, K_5, I_5, J_5) → poly69, a_{33}, d_{46}, k_{33}, i_{33}, j_{39}Polygon(B_{16}, B_5, J_1, I_1, D_5) → poly70, b_{41}, b_{42}, j_{40}, i_{34}, d_{47}Segment(R_3, C_4) → h_{33}Polygon(J_1, B_5, M_1, N_1, T_{14}) → poly71, j_{41}, b_{43}, m_{34}, n_{33}, t_{33}Segment(N_1, O_3) → l_{33}Polygon(W_{14}, N_1, O_3, A, G_1) → poly72, w_{11}, n_{34}, o_6, a_{34}, g_{36}Segment(K_1, T_1) → p_{33}Polygon(U_{14}, K_1, T_1, I_1, J_1) → poly73, u_8, k_{34}, t_{34}, i_{35}, j_{42}Polygon(V_{14}, G_1, E_1, B, K_1) → poly74, v_{11}, g_{37}, e_{37}, b_{44}, k_{35}Segment(O_5, S_1) → q_{33}Polygon(G_5, U_4, U_{15}, W_4, F_5) → poly75, g_{38}, u_9, u_{10}, w_{12}, f_{38}Polygon(V_{15}, Z_4, N_3, M_1, U_4) → poly76, v_{12}, z_6, n_{35}, m_{35}, u_{11}Segment(O_4, J_4) → r_{33}Segment(L_4, W_4) → s_{33}Polygon(W_{15}, O_4, J_4, Q_3, Z_4) → poly77, w_{20}, o_7, j_{43}, q_{34}, z_7Intersect(s_5, t_5) → O_{20}Polygon(T_{15}, O_4, O_{20}, L_4, W_4) → poly78, t_{35}, o_8, o_{20}, l_{34}, w_{21}Segment(L_3, F_3) → c_{34}Polygon(O_3, Q_{14}, P_{14}, N_3, M_1, N_1) → poly79, o_9, q_{35}, p_{34}, n_{36}, m_{36}, n_{37}Polygon(R_{14}, L_3, F_3, A, O_3) → poly80, r_{34}, l_{35}, f_{39}, a_{35}, o_{10}Polygon(P_{14}, R_3, Q_3, Z_4, N_3) → poly81, p_{35}, r_{35}, q_{36}, z_8, n_{38}Polygon(R_3, C_4, G, L_3, S_{14}) → poly82, r_{36}, c_{35}, g_{39}, l_{36}, s_{34}Segment(R_5, N_5) → h_{34}Segment(H_2, R_1) → h_{35}Polygon(C_{15}, P_1, B, K_1, T_1) → poly83, c_{36}, p_{36}, b_{45}, k_{36}, t_{36}Polygon(V, P_1, B_{15}, R_1, D) → poly84, v_{20}, p_{37}, b_{46}, r_{37}, d_{48}Polygon(R_1, A_{15}, S_1, I, H_2) → poly85, r_{38}, a_{36}, s_{35}, i_{36}, h_{36}Polygon(Z_{14}, T_1, I_1, O_5, S_1) → poly86, z_9, t_{37}, i_{37}, o_{11}, s_{36}Polygon(O_5, I_1, D_5, K_5, G_{16}, F_{16}) → poly87, o_{12}, i_{38}, d_{49}, k_{37}, g_{40}, f_{40}Polygon(F_{16}, N_5, I, S_1, O_5) → poly88, f_{41}, n_{39}, i_{39}, s_{37}, o_{21}Polygon(N_5, E_{16}, M_5, J, R_5) → poly89, n_{40}, e_{38}, m_{37}, j_{44}, r_{39}Polygon(D_{16}, K_5, I_5, K_8, M_5) → poly90, d_{50}, k_{38}, i_{40}, k_{39}, m_{38}Segment(J_2, B_2) → a_{37}Segment(W_2, L_2) → c_{37}Segment(V_5, G_2) → h_{37}Polygon(H_2, G_{15}, J_2, D, R_1) → poly91, h_{38}, g_{41}, j_{45}, d_{51}, r_{40}Polygon(L_2, E, B_2, J_2, F_{15}) → poly92, l_{37}, e_{39}, b_{47}, j_{46}, f_{42}Polygon(D_{15}, E_{15}, F_{15}, G_{15}) → poly93, d_{52}, e_{40}, f_{43}, g_{42}Polygon(L_2, E_{15}, G_2, F_2, W_2) → poly94, l_{38}, e_{41}, g_{43}, f_{44}, w_{22}Polygon(D_{15}, H_2, I, V_5, G_2) → poly95, d_{53}, h_{39}, i_{41}, v_{21}, g_{44}Polygon(K_{16}, V_5, I, N_5, R_5) → poly96, k_{40}, v_{22}, i_{42}, n_{41}, r_{41}Polygon(J_{16}, V_5, G_2, F_2, Q_5) → poly97, j_{47}, v_{23}, g_{45}, f_{45}, q_{37}Polygon(I_{16}, U_5, T_5, E_6, Q_5) → poly98, i_{43}, u_{12}, t_{38}, e_{42}, q_{38}Polygon(H_{16}, U_5, S_8, J, R_5) → poly99, h_{40}, u_{20}, s_{38}, j_{48}, r_{42}Segment(B_3, Z_5) → a_{38}Segment(A_7, B_6) → c_{38}Segment(C_3, U_6) → p_{38}Segment(Q_2, U_2) → a_{39}Segment(T_6, W_6) → c_{39}Polygon(K_{15}, U_2, E, L_2, W_2) → poly100, k_{41}, u_{21}, e_{43}, l_{39}, w_{23}Polygon(H_{15}, W_2, F_2, Z_5, B_3) → poly101, h_{41}, w_{24}, f_{46}, z_{10}, b_{48}Polygon(I_{15}, C_3, U_6, A_3, B_3) → poly102, i_{44}, c_{40}, u_{22}, a_{40}, b_{49}Polygon(J_{15}, U_2, Q_2, F, C_3) → poly103, j_{49}, u_{23}, q_{39}, f_{47}, c_{41}Segment(K_6, P_6) → m_{39}Segment(Q_6, V_6) → p_{39}Polygon(U_6, O_{15}, P_6, F, C_3) → poly104, u_{24}, o_{22}, p_{40}, f_{48}, c_{42}Polygon(P_6, K_6, J_6, Q_6, N_{15}) → poly105, p_{41}, k_{42}, j_{50}, q_{40}, n_{42}Polygon(Q_6, V_6, S_6, T_6, M_{15}) → poly106, q_{41}, v_{24}, s_{39}, t_{39}, m_{40}Polygon(L_{15}, U_6, A_3, W_6, T_6) → poly107, l_{40}, u_{25}, a_{41}, w_{25}, t_{40}Polygon(E_6, O_{16}, Z_5, F_2, Q_5) → poly108, e_{44}, o_{23}, z_{11}, f_{49}, q_{42}Polygon(Z_5, N_{16}, B_6, A_3, B_3) → poly109, z_{12}, n_{43}, b_{50}, a_{42}, b_{51}Polygon(M_{16}, B_6, A_7, C_6, D_6) → poly110, m_{41}, b_{52}, a_{43}, c_{43}, d_{54}Polygon(D_6, L_{16}, E_6, T_5, C_9) → poly111, d_{55}, l_{41}, e_{45}, t_{41}, c_{44}Segment(H_9, E_7) → s_{40}Segment(C_7, B_7) → s_{41}Polygon(A_7, S_{16}, W_6, A_3, B_6) → poly112, a_{44}, s_{42}, w_{26}, a_{45}, b_{53}Polygon(P_{16}, A_7, C_6, H_9, E_7) → poly113, p_{42}, a_{46}, c_{45}, h_{42}, e_{46}Polygon(C_7, Q_{16}, E_7, D_7, B_7) → poly114, c_{46}, q_{43}, e_{47}, d_{56}, b_{54}Polygon(R_{16}, W_6, T_6, S_6, C_7) → poly115, r_{43}, w_{27}, t_{42}, s_{43}, c_{47}Segment(I_4, S_4) → l_{42}Segment(Q_4, K_4) → m_{42}Segment(F_7, M_4) → h_{43}Polygon(J_4, Q_{15}, M_4, O_{20}, O_4) → poly116, j_{51}, q_{44}, m_{43}, o_{24}, o_{25}Polygon(P_{15}, Q_4, P_4, F_7, M_4) → poly117, p_{43}, q_{45}, p_{44}, f_{50}, m_{44}Polygon(S_{15}, S_4, G_4, K_4, Q_4) → poly118, s_{44}, s_{45}, g_{46}, k_{43}, q_{46}Polygon(R_{15}, S_4, I_4, Q_3, J_4) → poly119, r_{44}, s_{46}, i_{45}, q_{47}, j_{52}Segment(U_3, E_4) → l_{43}Segment(H_4, D_4) → t_{43}Polygon(N_{14}, E_4, U_3, G, C_4) → poly120, n_{44}, e_{48}, u_{26}, g_{47}, c_{48}Polygon(C_4, M_{14}, I_4, Q_3, R_3) → poly121, c_{49}, m_{45}, i_{46}, q_{48}, r_{45}Polygon(L_{14}, H_4, G_4, S_4, I_4) → poly122, l_{44}, h_{44}, g_{48}, s_{47}, i_{47}Polygon(O_{14}, H_4, D_4, H, E_4) → poly123, o_{26}, h_{45}, d_{57}, h_{46}, e_{49}Segment(W_3, T_3) → k_{44}Segment(S_3, K_3) → t_{44}Segment(A_4, V_3) → k_{45}Polygon(U_3, K_{13}, W_3, H, E_4) → poly124, u_{27}, k_{46}, w_{28}, h_{47}, e_{50}Polygon(J_{13}, A_4, Z_3, T_3, W_3) → poly125, j_{53}, a_{47}, z_{16}, t_{45}, w_{29}Polygon(S_3, H_{13}, U_3, G, K_3) → poly126, s_{48}, h_{48}, u_{28}, g_{49}, k_{47}Polygon(I_{13}, A_4, V_3, H_3, S_3) → poly127, i_{48}, a_{48}, v_{25}, h_{49}, s_{49}Segment(I_3, G_3) → l_{45}Polygon(N_{13}, I_3, H_3, S_3, K_3) → poly128, n_{45}, i_{49}, h_{50}, s_{50}, k_{48}Polygon(M_{13}, I_3, G_3, C, D_3) → poly129, m_{46}, i_{50}, g_{50}, c_{50}, d_{58}Polygon(D_3, L_{13}, F_3, A, Z) → poly130, d_{59}, l_{46}, f_{51}, a_{49}, z_{20}Polygon(F_3, O_{13}, K_3, G, L_3) → poly131, f_{52}, o_{27}, k_{49}, g_{51}, l_{47}Polygon(R_{13}, C_1, C, D_3, Z) → poly132, r_{46}, c_{51}, c_{52}, d_{60}, z_{21}Polygon(Q_{13}, C_1, F_1, P, A_1) → poly133, q_{49}, c_{53}, f_{53}, p_{45}, a_{50}Polygon(P_{13}, A_1, Q, B, E_1) → poly134, p_{46}, a_{51}, q_{50}, b_{55}, e_{51}Polygon(E_1, S_{13}, Z, A, P_{20}) → poly135, e_{52}, s_{51}, z_{22}, a_{52}, p_{47}Segment(O, W) → n_{46}Polygon(Q, V_{13}, O, P, A_1) → poly136, q_{51}, v_{26}, o, p_{48}, a_{53}Polygon(U_{13}, O, W, S, T) → poly137, u_{29}, o_{28}, w, s_{52}, t_{46}Polygon(T_{13}, V, D, D_2, T) → poly138, t_{47}, v_{27}, d_{61}, d_{62}, t_{48}Polygon(W_{13}, Q, B, P_1, V) → poly139, w_{30}, q_{52}, b_{56}, p_{49}, v_{28}Segment(M_2, R_2) → m_{47}Polygon(B_{14}, V_1, S, T, D_2) → poly140, b_{57}, v_{29}, s_{53}, t_{49}, d_{63}Polygon(C_{14}, D_2, D, J_2, B_2) → poly141, c_{54}, d_{64}, d_{65}, j_{54}, b_{58}Polygon(Z_{13}, A_2, O_2, E, B_2) → poly142, z_{23}, a_{54}, o_{29}, e_{53}, b_{59}Segment(V_1, C_2) → n_{47}Polygon(A_{14}, V_1, C_2, Z_1, A_2) → poly143, a_{55}, v_{30}, c_{55}, z_{24}, a_{56}Polygon(F_{14}, M_2, Z_1, A_2, O_2) → poly144, f_{54}, m_{48}, z_{25}, a_{57}, o_{30}Polygon(E_{14}, T_2, S_2, R_2, M_2) → poly145, e_{54}, t_{50}, s_{54}, r_{47}, m_{49}Polygon(T_2, D_{14}, G_{14}, Q_2, F, H_6) → poly146, t_{51}, d_{66}, g_{52}, q_{53}, f_{55}, h_{51}Polygon(Q_2, G_{14}, O_2, E, U_2) → poly147, q_{54}, g_{53}, o_{31}, e_{55}, u_{30}Segment(N_6, L_6) → l_{48}Segment(M_6, I_6) → n_{48}Polygon(H_6, J_{14}, N_6, S_2, T_2) → poly148, h_{52}, j_{55}, n_{49}, s_{55}, t_{52}Polygon(K_6, K_{14}, H_6, F, P_6) → poly149, k_{50}, k_{51}, h_{53}, f_{56}, p_{50}Polygon(H_{14}, M_6, I_6, J_6, K_6) → poly150, h_{54}, m_{50}, i_{51}, j_{56}, k_{52}Polygon(M_6, I_{14}, N_6, L_6, G_6) → poly151, m_{51}, i_{52}, n_{50}, l_{49}, g_{54}Segment(A_8, N_4) → r_{48}Segment(J_7, L_7) → r_{49}Segment(O_7, H_7) → l_{50}Segment(O_9, D_8) → r_{50}Segment(I_8, W_7) → l_{51}Segment(T_9, H_8) → n_{51}Polygon(W_{16}, F_7, P_4, L_7, J_7) → poly152, w_{31}, f_{57}, p_{51}, l_{52}, j_{57}Polygon(V_{16}, F_7, M_4, O_{20}, N_4) → poly153, v_{31}, f_{58}, m_{52}, o_{32}, n_{52}Polygon(N_4, U_{16}, H_7, G_7, A_8) → poly154, n_{53}, u_{31}, h_{55}, g_{55}, a_{58}Polygon(H_7, T_{16}, J_7, I_7, O_7) → poly155, h_{56}, t_{53}, j_{58}, i_{53}, o_{33}Polygon(C_{17}, L_4, W_4, F_5, W_7) → poly156, c_{56}, l_{53}, w_{32}, f_{59}, w_{33}Polygon(D_{17}, L_4, O_{20}, N_4, A_8) → poly157, d_{67}, l_{54}, o_{34}, n_{54}, a_{59}Polygon(D_8, B_{17}, W_7, I_8, C_8) → poly158, d_{68}, b_{60}, w_{34}, i_{54}, c_{57}Polygon(D_8, A_{17}, A_8, G_7, O_9) → poly159, d_{69}, a_{60}, a_{61}, g_{56}, o_{35}Segment(L_8, F_8) → r_{51}Polygon(H_{17}, I_8, W_7, F_5, V_4) → poly160, h_{57}, i_{55}, w_{35}, f_{60}, v_{32}Polygon(G_{17}, F_8, I_5, J_5, V_4) → poly161, g_{57}, f_{61}, i_{56}, j_{59}, v_{33}Polygon(F_8, F_{17}, H_8, G_8, L_8) → poly162, f_{62}, f_{63}, h_{58}, g_{58}, l_{55}Polygon(H_8, E_{17}, I_8, C_8, T_9) → poly163, h_{59}, e_{56}, i_{57}, c_{58}, t_{54}Polygon(K_{17}, K_8, M_5, J, P_8) → poly164, k_{53}, k_{54}, m_{53}, j_{60}, p_{52}Polygon(L_{17}, L_8, F_8, I_5, K_8) → poly165, l_{56}, l_{57}, f_{64}, i_{58}, k_{55}Polygon(J_{17}, P_8, T_8, M_8, N_8) → poly166, j_{61}, p_{53}, t_{55}, m_{54}, n_{55}Polygon(N_8, I_{17}, L_8, G_8, D_{10}) → poly167, n_{56}, i_{59}, l_{58}, g_{59}, d_{70}Polygon(T_5, U_5, S_8, O_{17}, V_8) → poly168, t_{56}, u_{32}, s_{56}, o_{36}, v_{34}Polygon(V_8, N_{17}, Z_8, W_8, D_9) → poly169, v_{35}, n_{57}, z_{26}, w_{36}, d_{71}Polygon(M_{17}, T_8, M_8, L_{10}, Z_8) → poly170, m_{55}, t_{57}, m_{56}, l_{59}, z_{27}Polygon(P_{17}, T_8, P_8, J, S_8) → poly171, p_{54}, t_{58}, p_{55}, j_{62}, s_{57}Polygon(S_{17}, C_9, D_6, C_6, B_9) → poly172, s_{58}, c_{59}, d_{72}, c_{60}, b_{61}Polygon(B_9, R_{17}, G_9, K, J_9) → poly173, b_{62}, r_{52}, g_{60}, k_{56}, j_{63}Polygon(G_9, Q_{17}, D_9, W_8, R_{10}) → poly174, g_{61}, q_{55}, d_{73}, w_{37}, r_{53}Polygon(T_{17}, C_9, T_5, V_8, D_9) → poly175, t_{59}, c_{61}, t_{60}, v_{36}, d_{74}Segment(I_9, K_9) → r_{54}Polygon(J_9, V_{17}, H_9, C_6, B_9) → poly176, j_{64}, v_{37}, h_{60}, c_{62}, b_{63}Polygon(U_{17}, H_9, E_7, D_7, I_9) → poly177, u_{33}, h_{61}, e_{57}, d_{75}, i_{60}Polygon(I_9, K_9, L_9, M_9, Z_{17}) → poly178, i_{61}, k_{57}, l_{60}, m_{57}, z_{28}Polygon(W_{17}, M_9, F_{11}, K, J_9) → poly179, w_{38}, m_{58}, f_{65}, k_{58}, j_{65}Segment(A_{11}, C_{11}) → r_{55}Segment(Q_7, U_7) → p_{56}Segment(H_{11}, R_7) → q_{56}Segment(Q_9, N_7) → r_{56}Segment(V_9, R_{11}) → p_{57}Segment(S_{11}, I_{11}) → q_{57}Segment(Z_{11}, P_{11}) → r_{57}Segment(A_{10}, W_{11}) → e_{58}Segment(C_{12}, K_{12}) → n_{58}Polygon(D_{18}, O_7, H_7, G_7, N_7) → poly180, d_{76}, o_{37}, h_{62}, g_{62}, n_{59}Polygon(C_{18}, N_7, Q_9, S_7, R_7) → poly181, c_{63}, n_{60}, q_{58}, s_{59}, r_{58}Polygon(R_7, B_{18}, Q_7, P_7, H_{11}) → poly182, r_{59}, b_{64}, q_{59}, p_{58}, h_{63}Polygon(E_{18}, Q_7, U_7, I_7, O_7) → poly183, e_{59}, q_{60}, u_{34}, i_{62}, o_{38}Segment(Z_9, S_9) → k_{59}Segment(F_{10}, W_9) → m_{59}Polygon(H_{18}, O_9, D_8, C_8, S_9) → poly184, h_{64}, o_{39}, d_{77}, c_{64}, s_{60}Polygon(G_{18}, S_9, Z_9, U_9, V_9) → poly185, g_{63}, s_{61}, z_{29}, u_{35}, v_{38}Polygon(V_9, F_{18}, Q_9, S_7, R_{11}) → poly186, v_{39}, f_{66}, q_{61}, s_{62}, r_{60}Polygon(I_{18}, Q_9, N_7, G_7, O_9) → poly187, i_{63}, q_{62}, n_{61}, g_{64}, o_{40}Polygon(L_{18}, T_9, H_8, G_8, W_9) → poly188, l_{61}, t_{61}, h_{65}, g_{65}, w_{39}Polygon(K_{18}, W_9, F_{10}, L, A_{10}) → poly189, k_{60}, w_{40}, f_{67}, l_{62}, a_{62}Polygon(J_{18}, A_{10}, W_{11}, U_9, Z_9) → poly190, j_{66}, a_{63}, w_{41}, u_{36}, z_{30}Polygon(M_{18}, T_9, C_8, S_9, Z_9) → poly191, m_{60}, t_{62}, c_{65}, s_{63}, z_{31}Segment(D_{12}, I_{10}) → p_{59}Segment(M_{10}, J_{10}) → e_{60}Segment(M_{12}, O_{10}) → p_{60}Segment(W_{12}, L_{12}) → e_{61}Segment(N_{12}, A_{12}) → k_{61}Polygon(F_{10}, P_{18}, D_{10}, G_8, W_9) → poly192, f_{68}, p_{61}, d_{78}, g_{66}, w_{42}Polygon(O_{18}, D_{10}, N_8, M_8, J_{10}) → poly193, o_{41}, d_{79}, n_{62}, m_{61}, j_{67}Polygon(N_{18}, J_{10}, M_{10}, H_{10}, I_{10}) → poly194, n_{63}, j_{68}, m_{62}, h_{66}, i_{64}Polygon(Q_{18}, I_{10}, D_{12}, L, F_{10}) → poly195, q_{63}, i_{65}, d_{80}, l_{63}, f_{69}Polygon(M_{10}, U_{18}, L_{10}, M_8, J_{10}) → poly196, m_{63}, u_{37}, l_{64}, m_{64}, j_{69}Polygon(T_{18}, L_{10}, Z_8, W_8, K_{10}) → poly197, t_{63}, l_{65}, z_{32}, w_{43}, k_{62}Polygon(S_{18}, K_{10}, W_{10}, N_{10}, O_{10}) → poly198, s_{64}, k_{63}, w_{44}, n_{64}, o_{42}Polygon(O_{10}, R_{18}, M_{10}, H_{10}, M_{12}) → poly199, o_{43}, r_{61}, m_{65}, h_{67}, m_{66}Polygon(W_{10}, A_{19}, R_{10}, W_8, K_{10}) → poly200, w_{45}, a_{64}, r_{62}, w_{46}, k_{64}Polygon(Z_{18}, R_{10}, G_9, K, T_{10}) → poly201, z_{33}, r_{63}, g_{67}, k_{65}, t_{64}Polygon(W_{18}, T_{10}, B_{11}, U_{10}, V_{10}) → poly202, w_{47}, t_{65}, b_{65}, u_{38}, v_{40}Polygon(V_{10}, V_{18}, W_{10}, N_{10}, S_{12}) → poly203, v_{41}, v_{42}, w_{48}, n_{65}, s_{65}Polygon(B_{11}, C_{19}, F_{11}, K, T_{10}) → poly204, b_{66}, c_{66}, f_{70}, k_{66}, t_{66}Polygon(B_{19}, F_{11}, M_9, L_9, A_{11}) → poly205, b_{67}, f_{71}, m_{67}, l_{66}, a_{65}Polygon(E_{19}, A_{11}, C_{11}, D_{11}, E_{11}) → poly206, e_{62}, a_{66}, c_{67}, d_{81}, e_{63}Polygon(E_{11}, D_{19}, B_{11}, U_{10}, F_{13}) → poly207, e_{64}, d_{82}, b_{68}, u_{39}, f_{72}Segment(M_{11}, N_{11}) → p_{62}Segment(J_{11}, O_{11}) → p_{63}Segment(V_{11}, Q_{11}) → p_{64}Polygon(M_{11}, I_{19}, H_{11}, P_7, N_{11}) → poly208, m_{68}, i_{66}, h_{68}, p_{65}, n_{66}Polygon(J_{11}, F_{19}, M_{11}, L_{11}, O_{11}) → poly209, j_{70}, f_{73}, m_{69}, l_{67}, o_{44}Polygon(G_{19}, I_{11}, S_{11}, K_{11}, J_{11}) → poly210, g_{68}, i_{67}, s_{66}, k_{67}, j_{71}Polygon(H_{19}, H_{11}, R_7, S_7, I_{11}) → poly211, h_{69}, h_{70}, r_{64}, s_{67}, i_{68}Polygon(L_{19}, R_{11}, V_9, U_9, P_{11}) → poly212, l_{68}, r_{65}, v_{43}, u_{40}, p_{66}Polygon(K_{19}, P_{11}, Z_{11}, U_{11}, V_{11}) → poly213, k_{68}, p_{67}, z_{34}, u_{41}, v_{44}Polygon(V_{11}, J_{19}, S_{11}, K_{11}, Q_{11}) → poly214, v_{45}, j_{72}, s_{68}, k_{69}, q_{64}Polygon(M_{19}, S_{11}, I_{11}, S_7, R_{11}) → poly215, m_{70}, s_{69}, i_{69}, s_{70}, r_{66}Segment(H_{12}, B_{12}) → e_{65}Polygon(Z_{11}, Q_{19}, W_{11}, U_9, P_{11}) → poly216, z_{35}, q_{65}, w_{49}, u_{42}, p_{68}Polygon(P_{19}, W_{11}, A_{10}, L, C_{12}) → poly217, p_{69}, w_{50}, a_{67}, l_{69}, c_{68}Polygon(O_{19}, C_{12}, K_{12}, G_{12}, H_{12}) → poly218, o_{45}, c_{69}, k_{70}, g_{69}, h_{71}Polygon(H_{12}, N_{19}, Z_{11}, U_{11}, B_{12}) → poly219, h_{72}, n_{67}, z_{36}, u_{43}, b_{69}Segment(J_{12}, E_{12}) → e_{66}Polygon(U_{19}, D_{12}, L, C_{12}, K_{12}) → poly220, u_{44}, d_{83}, l_{70}, c_{70}, k_{71}Polygon(T_{19}, A_{12}, H_{10}, I_{10}, D_{12}) → poly221, t_{67}, a_{68}, h_{73}, i_{70}, d_{84}Polygon(A_{12}, S_{19}, J_{12}, I_{12}, N_{12}) → poly222, a_{69}, s_{71}, j_{73}, i_{71}, n_{68}Polygon(J_{12}, R_{19}, K_{12}, G_{12}, E_{12}) → poly223, j_{74}, r_{67}, k_{72}, g_{70}, e_{67}Segment(Q_{12}, R_{12}) → q_{66}Polygon(N_{12}, Z_{19}, M_{12}, H_{10}, A_{12}) → poly224, n_{69}, z_{37}, m_{71}, h_{74}, a_{70}Polygon(W_{19}, M_{12}, O_{10}, N_{10}, L_{12}) → poly225, w_{51}, m_{72}, o_{46}, n_{70}, l_{71}Polygon(V_{19}, L_{12}, W_{12}, P_{12}, Q_{12}) → poly226, v_{46}, l_{72}, w_{52}, p_{70}, q_{67}Polygon(Q_{12}, A_{20}, N_{12}, I_{12}, R_{12}) → poly227, q_{68}, a_{71}, n_{71}, i_{72}, r_{68}Segment(B_{13}, U_{12}) → e_{68}Segment(V_{12}, T_{12}) → t_{68}Polygon(D_{20}, W_{12}, L_{12}, N_{10}, S_{12}) → poly228, d_{85}, w_{53}, l_{73}, n_{72}, s_{72}Polygon(C_{20}, S_{12}, V_{10}, U_{10}, U_{12}) → poly229, c_{71}, s_{73}, v_{47}, u_{45}, u_{46}Polygon(B_{20}, V_{12}, M, B_{13}, U_{12}) → poly230, b_{70}, v_{48}, m_{73}, b_{71}, u_{47}Polygon(V_{12}, E_{20}, W_{12}, P_{12}, T_{12}) → poly231, v_{49}, e_{69}, w_{54}, p_{71}, t_{69}Segment(A_{13}, C_{13}) → q_{69}Polygon(B_{13}, H_{20}, F_{13}, U_{10}, U_{12}) → poly232, b_{72}, h_{75}, f_{74}, u_{48}, u_{49}Polygon(G_{20}, F_{13}, E_{11}, D_{11}, A_{13}) → poly233, g_{71}, f_{75}, e_{70}, d_{86}, a_{72}Polygon(A_{13}, F_{20}, E_{13}, D_{13}, C_{13}) → poly234, a_{73}, f_{76}, e_{71}, d_{87}, c_{72}Segment(E_{13}, G_{13}) → r_{69}Polygon(E_{13}, I_{20}, B_{13}, M, G_{13}) → poly235, e_{72}, i_{73}, b_{73}, m_{74}, g_{72}
AI Drawing Prompt Reference
Draw a stochastic fractal tiling based on the Pythagorean theorem, iteratively constructing right triangles of varying side lengths to fill a plane, demonstrating core mathematical concepts like the Pythagorean theorem, stochastic processes, statistics, step functions, and tangent lines, start by drawing two perpendicular line segments, then draw two perpendicular lines from their endpoints, mark points at the intersections, repeat this process, and finally connect these points with line segments to form a complex geometric pattern.
The prompt above was compiled from the original drawing commands and is for reference only.