Art of Mathematics – Visualization of Dynamical Systems

Dynamical systems are mathematical models used to describe the time-dependent position of a point's position in ambient space. For example, a dynamical system could be used to describe the movement of a swinging pendulum. The way the pendulum moves is based on the laws of physics, but trajectory, velocity, acceleration, etc changes over time. Over at the University of Liverpool is a series of visualizations by mathematicians around the world that shows such dynamical systems.

Lasse Rempe, a mathematician, describes the beauty of these visualization in this video on the BBC. Many more beautiful pieces in the video and explanation of the underlying structures.