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Mandelbrot Set First Period Zoom

Mandelbrot Set First Period Zoom
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2018-11-25 01:54
TrigonometryCoordinate GeometryLimitComplex NumberGeometric Construction
This example demonstrates the first period of the Mandelbrot set by zooming out to the limit. Core mathematical concepts include limits, logic, rotation, angles, linear equations, trigonometry, and quadratic equations. Construction highlights the use of GeoGebra commands and objects such as Point, Line, Rotate, Intersect, Circle, Tangent, LineBisector, and Mirror. Suitable for high school and above, for understanding fractal geometry and complex dynamics.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(g) → B
  3. Line(A, B) → f
  4. Rotate(f, n, A) → f'
  5. Intersect(f', g) → C
  6. Intersect(c, f', 2) → D
  7. Circle(C, D) → d
  8. Point(f) → E
  9. Circle(E, B) → e
  10. Intersect(e, f') → F, G
  11. Circle(G, D) → h
  12. Tangent(E, c) → i, j
  13. Intersect(g, j) → H
  14. Circle(H, B) → k
  15. Intersect(k, j) → I, J
  16. LineBisector(B, J) → l
  17. Intersect(l, f) → K
  18. Circle(K, J) → p
  19. Mirror(h, f) → h'

AI Drawing Prompt Reference

Draw a graph demonstrating the first period of the Mandelbrot set by zooming out to the limit. Start by drawing a line segment, then rotate it around one end to find intersections. Use these points to draw circles and find more intersections. Add tangent lines and their intersections, then draw circles and perpendicular bisectors. Finally, mirror one of the circles to complete the construction.
The prompt above was compiled from the original drawing commands and is for reference only.