Pendulum Gyrations


Meanderings of attractor basins for the forced damped pendulum, 2014, by Evelyn Sander and James A. Yorke. In this movie, we show how the basins of attraction of the forced damped pendulum change as the forcing amplitude is varied. Both the number and topology of the basins often change quite drastically, quickly changing from laminar to chaotic, and  in some cases with a surprising number of distinct attractors.

Links to the movie: 

YouTube version                   
High quality version, MOV 
High quality version, MP4

How this movie was made:

The animation sequence was made using the program  Dynamics. It contains 800 frames, evenly spaced from rho=1.5 to rho=3.5. Each frame has resolution 1920 x 1080 pixels. 

The gorey details for making this movie in Dynamics:

The following is the .dd file needed to create each frame of the animation. You can run these commands using the following command command line in Unix/Mac XQuartz :   

./dynamics PendulumMovie2Frames.dd

This will generate .PCX files, which can be made into an animation using ffmpeg. 

PendulumMovie2Frames.dd     This version of the dd file produces two frames. This allows for modification and experimentation before creating a large movie. 

PendulumMovie.dd   This version produces the 800 frame movie. It takes a very long time!

PendulumDDAnnotated.txt This version is an annotated version of the dd file explaining what each command does. 

Exploratory Hall Rm. 4408・Fax: (703) 993–1491・E-mail: esander at gmu dot edu 
Mailing Address: Dept. of Math. Sci. MS-3F2, GMU, 4400 University Drive, Fairfax, VA 22030, USA