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Complex Exponential Circle Fractal

Complex Exponential Circle Fractal
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2021-12-27 16:57
CircleComplex Number
This example demonstrates the generation of a complex exponential circle fractal. It involves core concepts of complex numbers, exponential functions, and fractal geometry. Using commands like rotation, dilation, and locus, users can dynamically explore the fractal generation process. Suitable for high school mathematics education and research.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Circle(A, B) → c
  4. Rotate(B, (speed^(0) * n)) → C0
  5. Dilate(C0, scale) → C'
  6. Circle(C', C0) → d
  7. Rotate(C0, (speed^(1) * n), C') → D1
  8. Dilate(D1, scale, C') → D'
  9. Circle(D', D1) → e
  10. Rotate(D1, (speed^(2) * n), D') → E2
  11. Dilate(E2, scale, D') → E'
  12. Circle(E', E2) → f
  13. Rotate(E2, (speed^(3) * n), E') → F3
  14. Dilate(F3, scale, E') → F'
  15. Circle(F', F3) → g
  16. Rotate(F3, (speed^(4) * n), F') → G4
  17. Dilate(G4, scale, F') → G'
  18. Circle(G', G4) → h
  19. Rotate(G4, (speed^(5) * n), G') → H5
  20. Dilate(H5, scale, G') → H'
  21. Circle(H', H5) → k
  22. Rotate(H5, (speed^(6) * n), H') → I6
  23. Dilate(I6, scale, H') → I6'
  24. Circle(I6', I6) → p
  25. Locus(I6', n) → loc1

AI Drawing Prompt Reference

Draw a complex exponential circle fractal, demonstrating core concepts of complex numbers, exponential functions, and fractal geometry. Start from the intersection of coordinate axes, draw a circle with the point on one axis as the center, then repeatedly rotate, scale, and draw circles to simulate the fractal generation process, creating a dynamic and intricate pattern.
The prompt above was compiled from the original drawing commands and is for reference only.