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3D 费马树分形

3D 费马树分形
几何画板及绘图内容加载中，请稍等……
2018-07-14 05:50
立体几何几何作图
该范例演示了3D费马树分形的生成过程。它涉及到了分形几何和勾股定理。通过使用Polygon, Sequence, Prism等命令，可以构造出具有自相似特性的3D树形结构。适合高中及以上学生或教师使用，用于几何作图和分形学习。

GeoGebra 命令及参数

  1. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  2. Sequence((abs(blue1 - blue0) / levels * i), i, 1, levels) → gradBlueList
  3. Sequence((abs(red1 - red0) / levels * i), i, 1, levels) → gradRedList
  4. Sequence((abs(green1 - green0) / levels * i), i, 1, levels) → gradGreenList
  5. Prism(poly1, size) → Prisma1, E, edgeAE, edgeBF, edgeCG, edgeDH, edgeEF, edgeFG, edgeGH, edgeEH, F, G, H, faceABFE, faceBCGF, faceCDHG, faceADHE, faceEFGH
  6. FractalPI(poly1, angle) → q1, q2
  7. Prism(q1, size) → b, I, edge1, edge2, edge3, edge4, edgeIJ, edgeJK, edgeKL, edgeIL, J, K, L, face1, face3, face4, face2, faceIJKL
  8. Prism(q2, size) → c, M, edge6, edge5, edge7, edge8, edgeMN, edgeNO, edgeOP, edgeMP, N, O, P, face5, face6, face8, face7, faceMNOP
  9. FractalPI(q2, angle) → q3, q4
  10. Prism(q3, size) → d, Q, edge9, edge10, edge11, edge12, edgeQR, edgeRS, edgeST, edgeQT, R, S, T, face9, face11, face12, face10, faceQRST
  11. Prism(q4, size) → e, U, edge14, edge13, edge15, edge16, edgeUV, edgeVW, edgeWZ, edgeUZ, V, W, Z, face13, face14, face16, face15, faceUVWZ
  12. FractalPI(q4, angle) → q5, q6
  13. Prism(q5, size) → j, A_1, edge17, edge18, edge19, edge20, edge21, edge23, edge24, edge22, B_1, C_1, D_1, face17, face19, face20, face18, face21
  14. Prism(q6, size) → k, E_1, edge26, edge25, edge27, edge28, edge29, edge31, edge32, edge30, F_1, G_1, H_1, face22, face23, face25, face24, face26
  15. FractalPI(q3, angle) → q7, q8
  16. Prism(q7, size) → l, I_1, edge33, edge34, edge35, edge36, edge37, edge39, edge40, edge38, J_1, K_1, L_1, face27, face29, face30, face28, face31
  17. Prism(q8, size) → m, M_1, edge42, edge41, edge43, edge44, edge45, edge47, edge48, edge46, N_1, O_1, P_1, face32, face33, face35, face34, face36
  18. FractalPI(q1, angle) → q9, q10
  19. Prism(q9, size) → n, Q_1, edge49, edge50, edge51, edge52, edge53, edge55, edge56, edge54, R_1, S_1, T_1, face37, face39, face40, face38, face41
  20. Prism(q10, size) → o, U_1, edge58, edge57, edge59, edge60, edge61, edge63, edge64, edge62, V_1, W_1, Z_1, face42, face43, face45, face44, face46
  21. FractalPI(q10, angle) → q11, q12
  22. Prism(q11, size) → p, A_2, edge65, edge66, edge67, edge68, edge69, edge71, edge72, edge70, B_2, C_2, D_2, face47, face49, face50, face48, face51
  23. Prism(q12, size) → q, E_2, edge74, edge73, edge75, edge76, edge77, edge79, edge80, edge78, F_2, G_2, H_2, face52, face53, face55, face54, face56
  24. FractalPI(q9, angle) → q13, q14
  25. Prism(q13, size) → r, I_2, edge81, edge82, edge83, edge84, edge85, edge87, edge88, edge86, J_2, K_2, L_2, face57, face59, face60, face58, face61
  26. Prism(q14, size) → s, M_2, edge90, edge89, edge91, edge92, edge93, edge95, edge96, edge94, N_2, O_2, P_2, face62, face63, face65, face64, face66

AI 绘图提示语参考

请绘制一个三维毕达哥拉斯树分形图形，该图形应包含一个主干和多个自相似分支，每个分支由棱柱状结构组成，基于毕达哥拉斯定理构建。构造顺序是从一个基础多边形开始，首先将其扩展为三维棱柱，然后递归地在顶部生成两个较小的分支，每个分支再类似地扩展，重复多次以形成复杂的树状结构，整体呈现出几何美感和分形特性。
以上提示语为根据原始绘图命令整理而来，仅供参考。