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Mandelbrot Set by MrJHardy

Mandelbrot Set by MrJHardy
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2020-03-14 20:31
FunctionComplex NumberGeometric Construction
This example demonstrates the generation of the Mandelbrot set, a fractal set in the complex plane. The Mandelbrot set showcases the beautiful properties of complex number iteration. Using the commands from the construction summary, we can see how to use GeoGebra to plot points in the complex plane, which are determined by specific iteration rules to belong to the Mandelbrot set. Suitable for high school and college mathematics enthusiasts studying complex numbers and fractal geometry.

GeoGebra Commands & Parameters

  1. Segment(c, z_1) → a
  2. Segment(z_1, z_2) → b
  3. Segment(z_2, z_3) → d
  4. Segment(z_3, z_4) → e
  5. Segment(z_4, z_5) → f
  6. Segment(z_5, z_6) → g
  7. Segment(z_6, z_7) → h
  8. Segment(z_7, z_8) → i
  9. Segment(z_8, z_9) → j
  10. Segment(z_9, z_10) → k
  11. Segment((0, 0), c) → m
  12. Segment(z_10, z_9) → n
  13. Segment(z_11, z_10) → p
  14. Segment(z_12, z_11) → q
  15. Segment(z_13, z_12) → r
  16. Segment(z_14, z_13) → s
  17. Segment(z_15, z_14) → t
  18. Segment(z_16, z_15) → a_1
  19. Segment(z_17, z_16) → b_1
  20. Segment(z_18, z_17) → c_1
  21. Segment(z_19, z_18) → d_1
  22. Segment(z_20, z_19) → e_1

AI Drawing Prompt Reference

Draw a fractal set in the complex plane to demonstrate the generation of the Mandelbrot set. Start from the origin and sequentially draw a series of line segments connecting adjacent points, forming a complex geometric structure. These segments are connected in order, creating a pattern composed of multiple continuous parts, ultimately revealing the beautiful shape of the Mandelbrot set.
The prompt above was compiled from the original drawing commands and is for reference only.