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Polygon Fractal with Iterative Triangle Construction
Geometric Iteration: The Step button shows the process step-by-step. Start runs it quickly.
- A random starting point is chosen inside the given regular polygon, along with a random vertex and one of its neighbouring vertices.
- The starting point is connected to these two vertices. Together with the corresponding polygon side, this forms a triangle.
- The chosen centre point of this triangle has to be computed. The resulting point is the start for the next iteration step, using the same procedure.
This process generates a fractal attractor (Type 1 to Type 4), depending on which triangle centre is used:
- Centroid, i.e. the intersection of the medians (default)
- Incenter, i.e. the intersection of the angle bisectors
- Incenter of the medial triangle of the original triangle
- Weighted centroid (similar to Type 1)
Experiments with the Geometry Machine
Try different polygons and test Types 1 to 4. A, B and C are the vertices of the construction triangle. A lies inside the polygon, while B and C are two adjacent vertices of the polygon. With the weighted centroid you can pull the attractor inward (Point A) or outward (Points B and C).
Note: Depending on the chosen polygon and type, some points may lie outside the polygon. Such points are not drawn, but the algorithm continues using them.
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© 2019 Ulrich Schwebinghaus