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Bifurcation Diagram of the Mandelbrot Set (Real Cases)

Bifurcation Diagram of the Mandelbrot Set (Real Cases)
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2019-07-09 21:08
CalculusComplex Number
This example demonstrates the bifurcation diagram of the Mandelbrot set in real cases. It involves complex numbers, bifurcation theory, and iterative functions. Using GeoGebra commands such as Circle, it constructs the bifurcation diagram. Suitable for high school mathematics education and research.

GeoGebra Commands & Parameters

  1. Circle((a, A1), 1 / C1) → B1
  2. Circle((a, A2), 1 / C2) → B2
  3. Circle((a, A3), 1 / C3) → B3
  4. Circle((a, A4), 1 / C4) → B4
  5. Circle((a, A5), 1 / C5) → B5
  6. Circle((a, A6), 1 / C6) → B6
  7. Circle((a, A7), 1 / C7) → B7
  8. Circle((a, A8), 1 / C8) → B8
  9. Circle((a, A9), 1 / C9) → B9
  10. Circle((a, A10), 1 / C10) → B10
  11. Circle((a, A11), 1 / C11) → B11
  12. Circle((a, A12), 1 / C12) → B12
  13. Circle((a, A13), 1 / C13) → B13
  14. Circle((a, A14), 1 / C14) → B14
  15. Circle((a, A15), 1 / C15) → B15
  16. Circle((a, A16), 1 / C16) → B16
  17. Circle((a, A17), 1 / C17) → B17
  18. Circle((a, A18), 1 / C18) → B18
  19. Circle((a, A19), 1 / C19) → B19
  20. Circle((a, A20), 1 / C20) → B20
  21. Circle((a, A21), 1 / C21) → B21
  22. Circle((a, A22), 1 / C22) → B22
  23. Circle((a, A23), 1 / C23) → B23
  24. Circle((a, A24), 1 / C24) → B24
  25. Circle((a, A25), 1 / C25) → B25
  26. Circle((a, A26), 1 / C26) → B26
  27. Circle((a, A27), 1 / C27) → B27
  28. Circle((a, A28), 1 / C28) → B28
  29. Circle((a, A29), 1 / C29) → B29
  30. Circle((a, A30), 1 / C30) → B30
  31. Circle((a, A31), 1 / C31) → B31
  32. Circle((a, A32), 1 / C32) → B32
  33. Circle((a, A33), 1 / C33) → B33
  34. Circle((a, A34), 1 / C34) → B34
  35. Circle((a, A35), 1 / C35) → B35

AI Drawing Prompt Reference

Draw the bifurcation diagram of the Mandelbrot set in real cases, based on complex numbers, bifurcation theory, and iterative functions. First, draw a series of circles with centers at points (a, A1) to (a, A35) and radii 1/C1 to 1/C35, which will form the main part of the bifurcation diagram.
The prompt above was compiled from the original drawing commands and is for reference only.