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Substitution Fractal

Substitution Fractal
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2022-06-26 18:48
PolygonVectorGeometric Construction
This example demonstrates the generation process of a fractal. A fractal is a geometric shape that exhibits similar patterns at increasingly smaller scales. The example uses polygon and vector commands to generate a fractal through substitution rules. Suitable for high school and above students to learn fractal geometry and geometric construction.

GeoGebra Commands & Parameters

  1. Polygon((-1, -1), (1, -1), 4) → poly1
  2. Sequence(Dilate[Rotate[stroke1, (u * π / 2)], 1 / 2, Element[P, u]], u, 1, 4) → l1
  3. Sequence(Dilate[Rotate[l1, (u * π / 2)], 1 / 2, Element[P, u]], u, 1, 4) → l2
  4. Sequence(Dilate[Rotate[l2, (u * π / 2)], 1 / 2, Element[P, u]], u, 1, 4) → l3
  5. Sequence(Dilate[Rotate[l3, (u * π / 2)], 1 / 2, Element[P, u]], u, 1, 4) → l4
  6. Polygon(P) → q1

AI Drawing Prompt Reference

Draw a fractal pattern by starting with a square, then iteratively replacing each edge with a smaller, rotated square through scaling and rotation, repeating this process four times to create a complex fractal structure that exhibits self-similarity.
The prompt above was compiled from the original drawing commands and is for reference only.