Index of /~cheritat/MatMovies

 Name                    Last modified      Size  Description
 Parent Directory                             -   
 AdamExamplePer10/       03-Jul-2007 15:15    -   
 AirplaneDendrite/       10-Jun-2007 19:33    -   
 AirplanePrim4/          13-Jun-2007 13:58    -   
 AirplaneRabbit/         12-Oct-2007 10:34    -   
 Bug/                    20-Jun-2007 11:39    -   
 Deg3Newton/             05-Mar-2009 22:01    -   
 Den_1_6_Den_5_14/       05-Jun-2007 23:57    -   
 DendriteDendrite/       12-Oct-2007 10:26    -   
 DendriteOtherdendrite/  12-Oct-2007 10:21    -   
 DendriteRabbit/         12-Oct-2007 10:20    -   
 RabbitBasilica/         12-Oct-2007 00:02    -   
 RabbitPrim4/            12-Oct-2007 10:35    -   
 RabbitRabbit/           24-Feb-2009 14:23    -   
 ReesSharedExample/      12-Oct-2007 00:11    -   
 Siegels/                12-Oct-2007 10:40    -   
 Tuning/                 23-Feb-2008 14:25    -

Polynomial matings on the Riemann sphere

Welcome. I did not work out thumbnails yet. Here's a little guide throughout the directory structure of MatMovies.

You'll find in these directories various animations. You may like to browse them according to the following list.

Ray numbers: they indicate the argument of external rays tending to the parameter in the Miziurewicz case ( <=> strictly preperiodic critical point => subhyperbolic polynomial and dendrite Julia set). In the hyperbolic case ( <=> periodic critical point => Julia set enclosing bounded components of Fatou set ) there are two external rays indicated, and they land not on the parameter but on another one, which is the root of the hyperbolic component containing the correct parameter.

RabbitBasilica = mating of Douady's rabbit (ray=1/7 and 2/7) with the basilica (ray=1/3 and 2/3). The original example of mating.
RabbitRabbit = mating of Douady's rabbit (ray=1/7 and 2/7) with another Douady's rabbit.
RabbitPrim4 = mating of the Rabbit (1/7,2/7) with a period 4 primitive example in the 1/3 limb (ray=3/15 and 4/15).
AirplaneRabbit = the Airplane (3/7,4/7) with the rabbit (1/7,2/7). This one has longer ray connexions, leading to a limit where it is hard to recognize the two original Julia sets.
DendriteDendrite = a miziurewicz (ray=1/4) mated with an identical copy (ray=1/4 again). The limit is a Lattes example, it has a "regular" invariant measure (it is kind of evenly distributed) and is moreover related to the dragon area filling fractal curve. This is an example of Milnor.
DendriteOtherdendrite If one mates 1/4 with 1/6 instead, the limit looks much less regular.
DendriteRabbit = The 1/6 Mizurewicz with (1/7,2/7).
AirplanePrim4 = Airplaine (3/7,4/7) with period 4 primitive copy in the 1/3 limb (3/15,4/15). See how intricate this gets. This is another example of shared mating.
ReesSharedExamples = an example of shared matings.
Deg3Newton = Mating two particular degree 3 polynomials leads to the Julia set of a Newton method of another degree 3 polynomial (communicated by Tan Lei).
Siegels = Mating Siegel disks.
Tunings = Polynomial tuning is a close relative of polynomial mating.
...