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 5), depending on which triangle centre is used:

1. Centroid, i.e. the intersection of the medians (default)
2. Incenter, i.e. the intersection of the angle bisectors
3. Incenter of the medial triangle of the original triangle
4. Weighted centroid (similar to Type 1)
5. Snowflake starting at a polygon vertex, a random other vertex is chosen. The new point is placed on the connecting line at a fixed fraction of its length, measured from the current point (60 % for a hexagon, 50 % for a pentagon, and so on).