MathPlotAI Logo MathPlotAI

Fractal Length Calculation

Fractal Length Calculation
Loading the math board and drawing, please wait…
2020-05-23 04:02
TriangleVectorCoordinate GeometryInequality
This example demonstrates how to calculate the length of a fractal using GeoGebra; involves core math concepts like Fractal Geometry, Right Triangles, Inequalities, Vectors 2D, Standard Deviation, and Differential Equations; constructed using commands/objects such as Point, Flatten, PolyLine, Distance, Midpoint, Vector; suitable for high school and above learners to understand the complexity and calculation methods of fractal geometry.

GeoGebra Commands & Parameters

  1. Point(Ray[A, A + (1, 0)]) → B
  2. Flatten(Sequence[{Element[A1, i], Dilate[Element[A1, i + 1], 0.3333333333333333, Element[A1, i]], Rotate[Dilate[Element[A1, i + 1], 0.6666666666666666, Element[A1, i]], 1.0471975511965976, Dilate[Element[A1, i + 1], 0.3333333333333333, Element[A1, i]]], Dilate[Element[A1, i + 1], 0.6666666666666666, Element[A1, i]], Element[A1, i + 1]}, i, 1, Length[A1] - 1]) → A2
  3. Flatten(Sequence[{Element[A2, i], Dilate[Element[A2, i + 1], 0.33, Element[A2, i]], Rotate[Dilate[Element[A2, i + 1], 0.67, Element[A2, i]], 1.05, Dilate[Element[A2, i + 1], 0.33, Element[A2, i]]], Dilate[Element[A2, i + 1], 0.67, Element[A2, i]], Element[A2, i + 1]}, i, 1, Length[A2] - 1]) → A3
  4. Flatten(Sequence[{Element[A3, i], Dilate[Element[A3, i + 1], 0.33, Element[A3, i]], Rotate[Dilate[Element[A3, i + 1], 0.67, Element[A3, i]], 1.05, Dilate[Element[A3, i + 1], 0.33, Element[A3, i]]], Dilate[Element[A3, i + 1], 0.67, Element[A3, i]], Element[A3, i + 1]}, i, 1, Length[A3] - 1]) → A4
  5. Flatten(Sequence[{Element[A4, i], Dilate[Element[A4, i + 1], 0.33, Element[A4, i]], Rotate[Dilate[Element[A4, i + 1], 0.67, Element[A4, i]], 1.05, Dilate[Element[A4, i + 1], 0.33, Element[A4, i]]], Dilate[Element[A4, i + 1], 0.67, Element[A4, i]], Element[A4, i + 1]}, i, 1, Length[A4] - 1]) → A5
  6. Flatten(Sequence[{Element[A5, i], Dilate[Element[A5, i + 1], 0.33, Element[A5, i]], Rotate[Dilate[Element[A5, i + 1], 0.67, Element[A5, i]], 1.05, Dilate[Element[A5, i + 1], 0.33, Element[A5, i]]], Dilate[Element[A5, i + 1], 0.67, Element[A5, i]], Element[A5, i + 1]}, i, 1, Length[A5] - 1]) → A6
  7. PolyLine(Cell[1, n + 1]) → b
  8. Flatten(Sequence[{Element[A6, i], Dilate[Element[A6, i + 1], 0.33, Element[A6, i]], Rotate[Dilate[Element[A6, i + 1], 0.670000000000001, Element[A6, i]], 1.05, Dilate[Element[A6, i + 1], 0.33, Element[A6, i]]], Dilate[Element[A6, i + 1], 0.670000000000001, Element[A6, i]], Element[A6, i + 1]}, i, 1, Length[A6] - 1]) → A7
  9. Distance(A, B) → a
  10. Midpoint(C, D) → E
  11. Vector(E, D) → u
  12. Vector(E, C) → v