Chaotic System in Circles Makes Fractals

Imagine two identical circles, and two balls - one in each - placed at almost, but not exactly the same position. Now, let them fall. At first, they appear to be following the same path - but soon, their trajectories will diverge. This is a chaotic system. And these tend to have rather beautiful patterns. So let's try to visualize it! To colour in a point, let a ball drop from it. And read off the colour after the N-th hit. To put non-integer values of N, track the time and revert to the last hit. Alternatively, we can project the ball onto the circle. Let's try measuring distance instead of time.

Channel: Nikita Fractal

Views: 30,309

Keywords: Fractals, Maths, Art, Beauty, Mandelbrot, Visualizations

Id: 3hBb1_qI_II

Length: 6min 17sec (377 seconds)

Published: Thu Apr 06 2023