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Chaos Fractal in Polygon

Chaos Fractal in Polygon
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2020-07-17 18:25
PolygonFunctionSequenceCoordinate Geometry
This example demonstrates a chaos fractal within a polygon. It involves fractal geometry, polygons, and quadrilaterals, as well as exponential functions. Using GeoGebra commands such as Sequence, Polygon, PointIn, and IterationList, complex fractal patterns can be constructed. Suitable for high school mathematics education and research.

GeoGebra Commands & Parameters

  1. Sequence((cos(((2 * k) * π / ecken)), sin(((2 * k) * π / ecken))), k, 0, ecken) → P
  2. Polygon(P) → S
  3. PointIn(S) → Q
  4. Sequence({P(k), P(k + 1)}, k, 1, ecken) → Z
  5. IterationList({TriangleCenter[Element[T, 1], Element[Z, x(Element[T, 2]), 1], Element[Z, x(Element[T, 2]), 2], DI(DreieckPunkt)], (Random[1, ecken], 0)}, T, {{Q, (Random[1, ecken], 0)}}, n) → M

AI Drawing Prompt Reference

Draw a chaos fractal inside a polygon by first generating the vertices' coordinates of the polygon, then connecting these vertices to form the polygon. Randomly select a point inside the polygon and use sequences and iteration lists to iteratively generate complex fractal patterns involving triangle centers and randomly chosen polygon vertices, resulting in a dynamic and evolving chaos fractal structure.
The prompt above was compiled from the original drawing commands and is for reference only.