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Fractal Curve 4 by Steve Phelps

Fractal Curve 4 by Steve Phelps
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2019-10-28 07:24
FunctionTransformation
This example demonstrates the generation process of Fractal Curve 4. It involves fractal geometry and power functions. Using the PolyLine and Rotate commands, a series of rotated points are constructed to form a complex fractal pattern. Suitable for high school and above students to learn fractal geometry and function transformations.

GeoGebra Commands & Parameters

  1. PolyLine(A, E, F, B) → f
  2. Rotate(A1, (4 * π / 3), B) → B1
  3. Rotate(Translate[A1, D - B], (2 * π / 3), D) → C1
  4. Rotate(Dilate[{A1, B1, C1}, 0.5], (-2 * π / 6)) → A2
  5. Rotate(A2, (4 * π / 3), B) → B2
  6. Rotate(Translate[A2, D - B], (2 * π / 3), D) → C2
  7. Rotate(Dilate[{A2, B2, C2}, 0.500000000000002], (-2 * π / 6)) → A3
  8. Rotate(A3, (4 * π / 3), B) → B3
  9. Rotate(Translate[A3, D - B], (2 * π / 3), D) → C3
  10. Rotate(Dilate[{A3, B3, C3}, 0.500000000000004], (-2 * π / 6)) → A4
  11. Rotate(A4, (4 * π / 3), B) → B4
  12. Rotate(Translate[A4, D - B], (2 * π / 3), D) → C4
  13. Rotate(Dilate[{A4, B4, C4}, 0.500000000000006], (-2 * π / 6)) → A5
  14. Rotate(A5, (4 * π / 3), B) → B5
  15. Rotate(Translate[A5, D - B], (2 * π / 3), D) → C5
  16. Rotate(Dilate[{A5, B5, C5}, 0.500000000000008], (-2 * π / 6)) → A6
  17. Rotate(A6, (4 * π / 3), B) → B6
  18. Rotate(Translate[A6, D - B], (2 * π / 3), D) → C6
  19. Rotate(Dilate[{A6, B6, C6}, 0.50000000000001], (-2 * π / 6)) → A7
  20. Rotate(A7, (4 * π / 3), B) → B7
  21. Rotate(Translate[A7, D - B], (2 * π / 3), D) → C7
  22. Rotate(Dilate[{A7, B7, C7}, 0.50000000000001], (-2 * π / 6)) → A8
  23. Rotate(A8, (4 * π / 3), B) → B8
  24. Rotate(Translate[A8, D - B], (2 * π / 3), D) → C8

AI Drawing Prompt Reference

Draw a fractal curve by repeatedly rotating, translating, and scaling a series of shapes. Start with an initial quadrilateral, then apply rotations and transformations to each shape, scaling it down each time, to create a complex, recursive fractal pattern that demonstrates transformations and power functions.
The prompt above was compiled from the original drawing commands and is for reference only.