Embedded Files
A movie for exponential convergence of circle packings.
A movie for exponential convergence of circle packings.
Julia set/limit set that are quasiconformal to circle packings
Julia set/limit set that are quasiconformal to circle packings
Self-bump on the main hyperbolic component
Self-bump on the main hyperbolic component
Coorespondence between graphs, reflection groups and anti-rational maps
Coorespondence between graphs, reflection groups and anti-rational maps
2 connected simple planar graph
Limit set of a kissing reflection group
Julia set of a critically fixed anti-rational map
Julia set of critically fixed anti-rational maps associated to Plantonic solids
Julia set of critically fixed anti-rational maps associated to Plantonic solids
Tetrahedron
Cube
Octahedron
Icosahedron
Dodecahedron
J-conjugate hyperbolic components
J-conjugate hyperbolic components
The Julia sets of two hyperbolic rational maps that are conjugate on their Julia sets, but are in different hyperbolic components. The rational map is of the form as above for sufficiently small t. There are two choices of cubic roots which gives the identification of the formula with Z_3 \times Z_3.
(0,0) is in the same hyperbolic component as (1,1) by moving t around 0 once. This turns out to be the only additional identification, thus the formula gives 3 J-conjugate hyperbolic components. One can see the Julia components are twisted in a different (and incompatible) rate.
Buried Sierpinski Carpet and Tree mapping schemes
Buried Sierpinski Carpet and Tree mapping schemes
Buried Sierpinski Carpet
Buried Sierpinski Carpet
The Julia set of a hyperbolic rational map with finitely connected Fatou sets. It contains a fixed Sierpinski carpet as a buried component.
Associated Tree mapping scheme
Associated Tree mapping scheme
The tree mapping scheme associated to the buried Sierpinski carpet example.
A 'nested mating' of z^4-1 and z^4-1.10658-0.24848i.
A 'nested mating' of z^4-1 and z^4-1.10658-0.24848i.
The outermost Julia component is an inverted copy of the Julia set of z^4-1.
A zoom to see the innermost Julia component is a copy of the Julia set of z^4-1.10658-0.24848.
A zoom to see the Julia component of the boundary of black region is a covering of the Julia set of z^4-1.10658-0.24848.
A zoom to see the Julia component of the boundary of pink region is a covering of the Julia set of z^4-1.
The Julia set of z^4-1.
The Julia set of z^4-1.10658-0.24848.
A 'nested mating' of a basilica and a rabbit.
A 'nested mating' of a basilica and a rabbit.
Nested mating of a basilica.
The Julia set of a basilica.
Nested mating of a rabbit.
The Julia set of a rabbit.
A movie from Cantor set of circle to mono nested mating of a basilica.
A movie from Cantor set of circle to mono nested mating of a basilica.
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