Stretched parabolic mirror #mathematics @MathDoctorMitchell

Uploaded July 2026 | Updated September 2026, 5 hours ago

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

Hyperbolic mirror rotating about focal point. #mathematics

Modes of a Circular Membrane - Combined Pairs

Chase Favorite Fish in 3D 50 Fish bumping into each other

Swarming Behaviors - Fixed Velocity and Proximity Matrix

Particle Swarm Optimization - Personal greater than Social

Chaos Game with 26 Vertices #mathematics

Chase Your Favorite Particle While Bumping into Each Other

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

Hyperbolic Mirror and its reflective properties

Jonathan Mitchell |

Stretched parabolic mirror #mathematics