Аттрактор Лоренца, построенный для 100 случайных стартовых точек. Расчёт выполнен программой, сделанной на основе https://jakevdp.github.io/blog/2013/02/16/animating-the-lorentz-system-in-3d/
The Lorenz Attractor is simulated using C++ and plotted by openGL+Glut. I hope you enjoy this video.
Movies from the supplementary info of the paper “Detecting Causality in Complex Ecosystems,” authored by George Sugihara, Robert May, Hao Ye, Chih-hao Hsieh, Ethan Deyle, Michael Fogarty, and Stephan Munch. Published Online September 20 2012 in Science Express:
This movie demonstrates the relationship between time series and dynamic attractors (manifolds, M).
This movie illustrates how Takens’ Theorem (19) can be used to reconstruct a shadow manifold MX from a single time series, and illustrates the 1:1 mapping between M and MX.
This movie explains how convergent cross mapping (CCM) estimates states across variables.
Chaos – A mathematical adventure It is a film about dynamical systems, the butterfly effect and chaos theory, intended for a wide audience. From Jos Leys, Étienne Ghys and Aurélien Alvarez, the makers of Dimensions, comes CHAOS, a math movie with nine 13-minute chapters. More information is available on the website: http://www.chaos-math.org/en/film