Uploaded December 2025 | Updated September 2026, 44 minutes ago
This animation, created using MATLAB, illustrates the fractal generated by "the Chaos Game" by varying the value of the coefficient, p.
When p is small, the next point (iterate) is close to the selected vertex since (1-p) is relatively large.
The self-similarity of the fractals is shown in the zoomed-in windows on the right.
In the case of 6 vertices, it appears as if the hexagon tips intersect when p=1/3. I have not confirmed this. Just a conjecture.
What is the threshold for p for other shapes?
This animation, created using MATLAB, illustrates the fractal generated by "the Chaos Game" by varying the value of the coefficient, p.
When p is small, the next point (iterate) is close to the selected vertex since (1-p) is relatively large.
The self-similarity of the fractals is shown in the zoomed-in windows on the right.
In the case of 6 vertices, it appears as if the hexagon tips intersect when p=1/3. I have not confirmed this. Just a conjecture.
What is the threshold for p for other shapes?
