Lorenz and the butterflies
I just tried out Three.js (http://threejs.org/
) for making a simple 3D curve depicting the Lorenz attractor. I have never used Three.js before and was pleasantly surprised to learn that it is possible to add a so-called point cloud. In addition to the simple curve, I could add a point cloud of 10,000 blue butterflies under the flow of the Lorenz attractor. Butterflies that start arbitrarily close to each other will soon spread out, but they will trace out the same visual pattern (the yellow/red pattern shown below). Due to the sensitivity of initial conditions (the starting positions), the subsequent positions of the butterflies are not predictable, even though the Lorenz equations that define their motion do not contain any randomness.
Interactive Lorenz Attractor: http://www.malinc.se/m/Lorenz.php