Swarming Behaviors - Random Movement and Inertia @MathDoctorMitchell

Uploaded August 2025 | Updated September 2026, 4 hours ago

This animation, created using MATLAB, illustrates how we began our research project with particles moving in a rectangular region. The first part shows particles moving with fixed velocity.

The second part includes a random adjustment to the velocity.

Swarming Behaviors - Random Movement and Inertia

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

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