Below are links to video animations in
three different formats: .flv (Flash), .wmv (Windows movie) and .mov
(Quicktime). These are all compressed from the original Mathematica output
which is uncompressed .avi at 720 by 480 resolution and 15 frames per second.
Each raw frame is a postscript image. Audio tracks are added with Adobe
Premier. See Animations.pdf for details.
Despite its large compression factor,
the flv format seems to give the best results for this type of highcontrast
animation. To get a free FLV player try the nonprofit videolan.org. This player is very popular
and will play other formats as well.
We also recommend the AVS Video Converter
for going back and forth between formats. It is surprising that conversions
from flv to mov or wmv are still of decent quality and yet very small in
size.
To download any of the files, follow
this link to the Animation Folder. To learn more
about projections see Projections.pdf
and also see the Summary files for the individual polygons in the PDF folder.
Christmas 2011

.flv

.wmv

.mov

The P2 projection of the S[1] 'bud' and its clones in the first 6
rings of N = 17. There is a companion CDF at N17Rings.

Duration ≈ 11 min.

Jude

.flv

.wmv

.mov

A P2 projection for N =13 showing the birth of symmetric episodes and
their demise. This appears to be a bounded nonperiodic orbit.

Duration ≈ 6 min.

Flower Basket

.flv

.wmv

.mov

A P2 projection for N =17 showing the prelude to a region of large
scale symmetry.The region shown here is about 10,000 by 8,000 units and
took over 400 million iterations to generate.

Duration ≈ 4.5 min.

Indian's Pink Poodle

.flv

.wmv

.mov

The P7 projection of an initial point in the 3rd ring of N = 17.
Symmetric episodes like this are
typically embedded in larger scale symmetry and for unbounded orbits the
scales may increase without limit.

Duration ≈ 4.5 min.

Time

.flv

.wmv

.mov

A P4 projection for N= 11 showing a portion of an orbit which has
few signs of stable behavior. This reflects the turbulent dynamics of this
4k+3 prime polygon.

Duration ≈ 4 min.

Roller Coaster

.flv

.wmv

.mov

A P7 projection for N= 17 using an initial point in the inner star
region. At the beginning of the animation, this point can be seen just to
the left of 'Mom'. There is no 'filtering' used in this algorithm so there
are minor embellishments caused by rotations.This portion of the orbit is
symmetric but the large scale dynamics are not symmetric.

Duration ≈ 5 min.

N5 Kite

.flv

.wmv

.mov

A P2 projection for the nonregular N5 Kite. This orbit may be unbounded.
The initial point shown here is about 2500 units from the origin but the
orbit began in close proximity to the origin. Points oscillate widely in
distance with a trend toward divergence. This type of 'semiperiodic
divergence' appears to be 'generic' for unbounded orbits.

Duration ≈ 4 min.

