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Sierpinski's Carpet

Sierpinski's Carpet
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2022-01-02 13:37
Polygon
This example demonstrates the construction of Sierpinski's Carpet, a fractal geometric shape. The construction involves repeatedly dividing a square into smaller squares and removing the central square at each iteration. Key GeoGebra commands used include Polygon and Midpoint. Suitable for high school mathematics education, particularly in geometry and fractal geometry.

GeoGebra Commands & Parameters

  1. Polygon((0, 0), (1, 0), 4) → poly1
  2. Polygon((1, 0), (2, 0), 4) → poly2
  3. Polygon((2, 0), (3, 0), 4) → poly3
  4. Polygon((0, 1), (1, 1), 4) → poly4
  5. Polygon((1, 2), (1, 1), 4) → poly5
  6. Polygon((2, 1), (3, 1), 4) → poly6
  7. Polygon((0, 2), (1, 2), 4) → poly7
  8. Polygon((1, 2), (2, 2), 4) → poly8
  9. Polygon((2, 2), (3, 2), 4) → poly9
  10. Midpoint(A, B) → E
  11. Midpoint(B, C) → F
  12. Midpoint(C, D) → G
  13. Midpoint(D, A) → H

AI Drawing Prompt Reference

Draw a fractal geometric shape starting with a large square, divide it into nine smaller squares, remove the central square, and repeat the process on the remaining smaller squares, showing a pattern similar to Sierpinski's Carpet by continuously removing the center squares and keeping the surrounding ones.
The prompt above was compiled from the original drawing commands and is for reference only.