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AR Pythagoras Tree

AR Pythagoras Tree
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2020-03-31 23:22
TriangleSequenceGeometric Construction
This is an AR Pythagoras tree example. It demonstrates the application of the Pythagorean theorem through fractal geometry, showing the generation process of a tree-like structure. It uses GeoGebra commands such as Polygon, Sequence, Prism to construct a dynamic fractal tree model. Suitable for high school mathematics teaching and learning, especially for the study of geometry and fractal theory.

GeoGebra Commands & Parameters

  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 Drawing Prompt Reference

Draw an AR Pythagoras tree by first creating a quadrilateral and then generating a dynamic fractal tree structure using different colored gradients to fill each fractal level polygon. Finally, construct multiple layers of prisms to form the tree structure.
The prompt above was compiled from the original drawing commands and is for reference only.