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Sierpinski Triangle by Luis Miguel López Herranz

Sierpinski Triangle by Luis Miguel López Herranz
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2016-01-22 03:08
Triangle
In collections Regularity
This example demonstrates the generation process of the Sierpinski triangle. It involves core concepts of fractal geometry, showing how self-similar geometric shapes are generated through iterative processes. It uses GeoGebra commands such as Ray, Circle, Intersect, Polygon, Vector, Sequence, and Join to construct a dynamic Sierpinski triangle. Suitable for high school and above students to learn fractal geometry and geometric construction.

GeoGebra Commands & Parameters

  1. Ray(A, B_1) → a
  2. Circle(A, l) → c
  3. Intersect(c, a, 1) → B
  4. Polygon(A, B, 3) → polígono1, b, d, e, C
  5. Vector(A, B) → u
  6. Sequence(Sequence[Polygon[A + (If[i ≤ 2^(j), i] * u / 2^(j)), A + (If[i ≤ 2^(j), i] * u / 2^(j)) + (l / 2^(j); 60°), A + (If[i ≤ 2^(j), i] * u / 2^(j)) + (l / 2^(j); 120°), A + (If[i ≤ 2^(j), i] * u / 2^(j))], i, 1, 2^(n), 2], j, 1, n) → lista1
  7. Vector(C, A) → v
  8. Vector(B, C) → w
  9. Join(lista1) → lista2
  10. RemoveUndefined(lista2) → lista3
  11. Sequence(Sequence[Translate[Take[lista3, 2^(i - 1), 2^(i) - 2 - j], Vector[((j + 1) * ((-v)) / 2^(i - 1))]], i, 2, n], j, 0, 2^(n)) → lista4