Particle Swarm Optimization - Large Inertial Coefficient @MathDoctorMitchell

Uploaded August 2025 | Updated September 2026, 39 minutes ago

This animation, created using MATLAB, illustrates the inertial component causing the acceleration of each of the particles (red). Both of the PERSONAL (green) and SOCIAL (blue) weights are relatively small.

The viewer can see how the particles exhibit high inertia. Yes, they change velocity based on the location of the personal or global best cost, but the resistance to change in motion causes more oscillatory behavior than would be typically desired by the programmer.

The dampening coefficient is removed; thus, the oscillations would, in theory, persist forever.

Particle Swarm Optimization - Large Inertial Coefficient

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

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$Fractals Produced by Varying p on the Chaos Game with 26 Vertices This animation, created using MATLAB, illustrates the resulting stable attractor generated by the Chaos Game with varying proportions p = 0 to p = 0.1. The self-similarity of the fractal is shown in the zoomed-in windows on the right. Research question: What is the precise proportion at which the 26-gons will intersect?$