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Tree Growth Iteration

Tree Growth Iteration
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2020-01-29 16:14
SequenceGeometric ConstructionSlider Animation
This example demonstrates the growth of a tree through iteration, showcasing the branching structure. Key mathematical concepts include sequences and iteration. Using commands like Branche_2, Segment, Branche3, Polygon, Line, etc., the branching structure of a tree can be constructed. Suitable for middle school and above students to learn geometric construction and the concept of iteration.

GeoGebra Commands & Parameters

  1. Branche_2(A, B, k, t) → C, D, e, f, E, F, G, H, a, b, c, d
  2. Segment(B, A) → g
  3. Branche_2(C, E, k, t) → I, J, m, n, K, L, M, N, h, i, j, l
  4. Branche_2(C, F, k, t) → O, P, a1, b1, Q, R, S, T, p, q, r, s
  5. Branche_2(D, G, k, t) → U, V, g1, h1, W, Z, A1, B1, c1, d1, e1, f1
  6. Branche_2(D, H, k, t) → C1, D1, m1, n1, E1, F1, G1, H1, i1, j1, k1, l1
  7. Branche3(k, t, P, S) → p1, q1, f2, g2, h2, i2, j2, k2, l2, m2, n2, p2, r1, q2, r2, s2, t2, a3, b3, c3, d3, e3, f3, s1, t1, a2, b2, c2, d2, e2
  8. Branche3(k, t, O, R) → g3, h3, r3, s3, t3, a4, b4, c4, d4, e4, f4, g4, i3, h4, i4, j4, k4, l4, m4, n4, p4, q4, r4, j3, k3, l3, m3, n3, p3, q3
  9. Branche3(k, t, O, Q) → s4, t4, i5, j5, k5, l5, m5, n5, p5, q5, r5, s5, a5, t5, a6, b6, c6, d6, e6, f6, g6, h6, i6, b5, c5, d5, e5, f5, g5, h5
  10. Branche3(k, t, J, N) → j6, k6, a7, b7, c7, d7, e7, f7, g7, h7, i7, j7, l6, k7, l7, m7, n7, p7, q7, r7, s7, t7, a8, m6, n6, p6, q6, r6, s6, t6
  11. Branche3(k, t, J, M) → b8, c8, l8, m8, n8, p8, q8, r8, s8, t8, a9, b9, d8, c9, d9, e9, f9, g9, h9, i9, j9, k9, l9, e8, f8, g8, h8, i8, j8, k8
  12. Branche3(k, t, I, L) → m9, n9, d10, e10, f10, g10, h10, i10, j10, k10, l10, m10, p9, n10, p10, q10, r10, s10, t10, a11, b11, c11, d11, q9, r9, s9, t9, a10, b10, c10
  13. Branche3(k, t, I, K) → e11, f11, p11, q11, r11, s11, t11, a12, b12, c12, d12, e12, g11, f12, g12, h12, i12, j12, k12, l12, m12, n12, p12, h11, i11, j11, k11, l11, m11, n11
  14. Branche3(k, t, P, T) → q12, r12, g13, h13, i13, j13, k13, l13, m13, n13, p13, q13, s12, r13, s13, t13, a14, b14, c14, d14, e14, f14, g14, t12, a13, b13, c13, d13, e13, f13
  15. Branche3(k, t, U, W) → h14, i14, s14, t14, a15, b15, c15, d15, e15, f15, g15, h15, j14, i15, j15, k15, l15, m15, n15, p15, q15, r15, s15, k14, l14, m14, n14, p14, q14, r14
  16. Branche3(k, t, V, A1) → t15, a16, j16, k16, l16, m16, n16, p16, q16, r16, s16, t16, b16, a17, b17, c17, d17, e17, f17, g17, h17, i17, j17, c16, d16, e16, f16, g16, h16, i16
  17. Branche3(k, t, V, B1) → k17, l17, b18, c18, d18, e18, f18, g18, h18, i18, j18, k18, m17, l18, m18, n18, p18, q18, r18, s18, t18, a19, b19, n17, p17, q17, r17, s17, t17, a18
  18. Branche3(k, t, C1, E1) → c19, d19, m19, n19, p19, q19, r19, s19, t19, a20, b20, c20, e19, d20, e20, f20, g20, h20, i20, j20, k20, l20, m20, f19, g19, h19, i19, j19, k19, l19
  19. Branche3(k, t, C1, F1) → n20, p20, e21, f21, g21, h21, i21, j21, k21, l21, m21, n21, q20, p21, q21, r21, s21, t21, a22, b22, c22, d22, e22, r20, s20, t20, a21, b21, c21, d21
  20. Branche3(k, t, D1, G1) → f22, g22, q22, r22, s22, t22, a23, b23, c23, d23, e23, f23, h22, g23, h23, i23, j23, k23, l23, m23, n23, p23, q23, i22, j22, k22, l22, m22, n22, p22
  21. Branche3(k, t, D1, H1) → r23, s23, h24, i24, j24, k24, l24, m24, n24, p24, q24, r24, t23, s24, t24, a25, b25, c25, d25, e25, f25, g25, h25, a24, b24, c24, d24, e24, f24, g24
  22. Branche3(k, t, U, Z) → i25, j25, t25, a26, b26, c26, d26, e26, f26, g26, h26, i26, k25, j26, k26, l26, m26, n26, p26, q26, r26, s26, t26, l25, m25, n25, p25, q25, r25, s25
  23. Polygon(E_1, D_1, B_1, C_1) → poly1, e_1, d_1, b_1, c_1
  24. Line(A, B_1) → a_1
  25. Point(a_1) → F_1
  26. Point(a_1) → G_1
  27. Polygon(G_1, F_1, 4) → poly2, g_1, f_1, h_1, i_1, H_1, I_1
  28. Sequence(((Random[-38, 10] * 0.6) + (0 * o), 32 - (i * o)), i, 0, 13, 0.1) → liste1

AI Drawing Prompt Reference

Draw a tree structure that grows through iteration, showcasing branching patterns. Start with a trunk and extend two main branches upward, each main branch further splits into two secondary branches, repeating this process recursively. Use lines of varying thickness and color to represent different levels of branches, connecting the base to a square and terminal ends of branches to circular nodes, creating a dynamic upward growth effect.
The prompt above was compiled from the original drawing commands and is for reference only.