Index of /~cheritat/MatMovies

Name	Last modified	Size

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	-
Magic/	14-Apr-2012 16:19	-
README.html	24-Feb-2009 14:37	2.4K
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.
...