Pushing Simulation to the Limit to Find Order in Chaos

In this video, the creator runs millions of double pendulum simulations to uncover order in chaos and generate a new fractal. The simulations use an 8th-order Dormand-Prince Runge-Kutta method for high accuracy, and the visualizations are created with Blender and Manim CE. The video also validates unexpected elements by varying parameters such as gravity, rod-length ratios, and pendulum masses, showing that certain chaotic regions persist. Timestamps: 0:00 Intro 0:49 3D Simulations of Order and Chaos 5:55 Laying the Groundwork and on Determinism 7:05 Plotting Order and Chaos 11:43 Visualizing All Possible Initial Positions 13:52 Pixel Visualization and the Islands of Stability 19:28 Flips and the Hidden Order in Chaos 24:21 Validation of Unexpected Elements 24:45 Zooming Shot Details 25:24 Only a Tourist’s Guide