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Mandelbrot Set

Mandelbrot Set
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2020-07-10 17:08
Coordinate Geometry
This example demonstrates the generation of the Mandelbrot set, a fractal geometry figure that exhibits infinite complexity and self-similarity. By dragging the 'Mandelbrush' tool, you can observe the fractal details in different areas. The construction uses basic GeoGebra objects like points and segments, suitable for high school and above students to learn fractal geometry.

GeoGebra Commands & Parameters

  1. Point A1(-1.6916720804518754, 0.9005472530285566)
  2. A1 + 0.05
  3. B1 + 0.05
  4. C1 + 0.05
  5. D1 + 0.05
  6. E1 + 0.05
  7. F1 + 0.05
  8. G1 + 0.05
  9. A1^(2) + A1
  10. A2^(2) + A1
  11. A3^(2) + A1
  12. A4^(2) + A1
  13. B1^(2) + B1
  14. B2^(2) + B1
  15. B3^(2) + B1
  16. B4^(2) + B1
  17. C1^(2) + C1
  18. C2^(2) + C1
  19. C3^(2) + C1
  20. C4^(2) + C1
  21. D1^(2) + D1
  22. D2^(2) + D1
  23. D3^(2) + D1
  24. D4^(2) + D1
  25. E1^(2) + E1
  26. F1^(2) + F1
  27. G1^(2) + G1
  28. H1^(2) + H1
  29. E2^(2) + E1
  30. E3^(2) + E1
  31. E4^(2) + E1
  32. F2^(2) + F1
  33. F3^(2) + F1
  34. F4^(2) + F1
  35. G2^(2) + G1
  36. G3^(2) + G1
  37. G4^(2) + G1
  38. H2^(2) + H1
  39. H3^(2) + H1
  40. H4^(2) + H1
  41. A5^(2) + A1
  42. C5^(2) + C1
  43. D5^(2) + D1
  44. E5^(2) + E1
  45. F5^(2) + F1
  46. G5^(2) + G1
  47. H5^(2) + H1
  48. test(x) = x ≟ x
  49. A6^(2) + A1
  50. A7^(2) + A1
  51. A8^(2) + A1
  52. A9^(2) + A1
  53. A10^(2) + A1
  54. A11^(2) + A1
  55. A12^(2) + A1
  56. A13^(2) + A1
  57. A14^(2) + A1
  58. A15^(2) + A1
  59. A16^(2) + A1
  60. A17^(2) + A1

AI Drawing Prompt Reference

Draw the Mandelbrot set starting from point A1 at (-1.6916720804518754, 0.9005472530285566), using the formula z = z^2 + c, where c is a point on the complex plane and z starts from 0. Gradually move the points to observe the details of the set.
The prompt above was compiled from the original drawing commands and is for reference only.