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Mandelbrot Set Reflection

Mandelbrot Set Reflection
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2019-02-13 09:24
FunctionComplex NumberTransformation
This example demonstrates the reflection of the Mandelbrot set across the line x=-3/4. Using an online image, we explore the symmetry of complex number sets. The construction involves commands like Mirror, Sequence, and Polygon. Suitable for high school and above students learning complex number transformations.

GeoGebra Commands & Parameters

  1. Mirror(Mirror[A, f], xAxis) → C
  2. Mirror(Mirror[B, f], xAxis) → D
  3. Sequence(Circle[(0, 1 - n / 2), 1 / 4], n, 0, 4) → l2
  4. Mirror(h, f) → i
  5. Mirror(g, xAxis) → g'
  6. Sequence(Circle[(0 - n / 2, 0), 1 / 4], n, -1, 4) → l1
  7. Polygon(E, F, G, H) → q1, e, f_1, g_1, h_1

AI Drawing Prompt Reference

Reflect the Mandelbrot set across the line x=-3/4, then reflect it again across the x-axis. Draw a series of circles with radius 1/4, centered at (0, 1 - n/2) and (0 - n/2, 0). Finally, create a quadrilateral using points E, F, G, and H.
The prompt above was compiled from the original drawing commands and is for reference only.