Julia set of z->(exp(z)-1)/2
Closeup of the Julia set of z->(exp(z)-1)/2
High resolution (for inkjet printers)
987 petals
A quad. Julia set with 987 parab. petals in approx. Fatou coord.
The cauliflower
Colorful cauliflower
Checked towel cauliflower filling
Quad. poly. with a parabolic fixed point with many petals
13/34 rot. nb. ind. fix. pt. Julia set.
(hi res)
34/89
(hi res)
Golden mean Siegel disk
Golden mean Siegel disk
(hi res)
Closeup on the critical point of the golden mean quadratic Siegel disk
(hi res)
Approx. domain of def. of the McMullen limit map
(hi res)
Quasiconformal models
Ghys model for the quad. gold. mean Sieg. disk.
(hi res)
Full Julia set of the previous Blaschke fraction.
(hi res)
Virtual Siegel disks
Virtual Siegel disk in the cauliflower
(hi res, color)
(lo res, grayscale)
Siegel disk tending to the previous
(hi res)
Virtual Siegel disk in the 2/5 rabbit
(hi res)
Pérez-Marco's Riemann sufaces
Uniformization of Pérez-Marco's tube-log Riemann surface
(hi res, color)
(lo res, grayscale)
(hi res, black and white)
Uniformization of another Riemann surface of Pérez-Marco
(hi res, color)
(lo res, grayscale)
(hi res, black and white)
Siegel disk of exp(z)+c
The golden mean fixed Siegel disk in the family exp(z)+c (lo res, grayscale)
(hi res, black and white)
Plus some of its invariant circles (medium, color)
(hi res, color)
Digitated Siegel disk
Digitated Siegel disk
Zakeri's Jordan curve
Zakeri's Jordan curve in a slice of the parameter space of cubic polynomials
Pseudo hedgehogs
A pseudo hedgehog
Another
Another
Another
Another
Near matings
Two mating polynomial Julia sets
Close-up on the previous one
Douady's rabbit mating with a dendrite
Near tunings
Tuning a dragon by a segment
... closer to the limit
A disconnected rational Julia set
A disconnected rational Julia set
Bifucation loci in parameter spaces
Mandelbrot sets everywhere
A Julia set equal to the Riemann sphere, looks like Jupiter's moon Callisto
A representation of the invariant measure associated to some post-critically finite rational map whose Julia set is the whole sphere.
Three representations of the same Julia sets with a Herman ring: z+a*sin(z)+t, with golden mean rotation number.
Julia set with a Herman ring
Same Julia set, shades of gray revealing more structure
Another representation
Parabolic renormalization
Shishikura's invariant class
exp
tan