Circle Map Movies

Like the Mandelbrot fractals, the circle map has a basin of attraction that can be viewed. This page contains movies that illustrate that basin of attraction.

The following are the same as the YouTube page, but with different formats/resolutions.

Short Blue (860 KBytes -- 60 frames)
Short Color (1.60 MBytes -- 60 frames)
Long Blue (4.80 MBytes -- 240 frames)
Long Color (7.45 MBytes -- 240 frames)

All of the above movies show the basin of attraction of
z(n+1) = z(n) + omega - K * sin (2 * pi * z(n))
with z, omega and K complex, and Re z(n) == Re z(n) mod 1 (i.e. we've wrapped the real part of z).
Re omega
Real part of omega -- Time axis -- i.e. Re omega = 0.0 at start of movie, and Re omega = 1.0 at end of movie.
Im omega
Imaginary part of omega -- zero for the entire movie.
Re K
plotted along horizontal axis -- runs from -0.5 on left side of frame, to +0.5 on right side of frame.
Im K
plotted along vertical axis -- is zero in the center. Aspect ratio is preserved -- i.e it runs from -0.5* (240/320) to +0.5 * (240/320)

Note that the movies are essentially symmetric about omega=0.5. The four movies above differ only in length, choice of colormap, and length of iteration (the long movies were iterated more, and thus have better resolution).


These movies show the interior measure of the circle map, with the parameters and values as explained at the top of this page.

The following are the same as the YouTube page, but with different formats/resolutions.

Short Measure (896K - 60 frames)
Bright Measure (2.52M - 60 frames)
Long Measure (2.53M - 240 frames)


Storyboard from the Long Color movie:


Storyboard from the Long Offset movie:


Storyboard from the Long Measure movie:


Copyright (c) 1996 Linas Vepstas

Creative Commons License
Circle Movies by Linas Vepstas is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.