Julia set of z->(exp(z)-1)/2
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| Closeup of the Julia set of z->(exp(z)-1)/2 |
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| High resolution (for inkjet printers) |
987 petals
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| A quad. Julia set with 987 parab. petals in approx. Fatou coord. |
The cauliflower
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| Colorful cauliflower |
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| Checked towel cauliflower filling |
Quad. poly. with a parabolic fixed point with many petals
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| 13/34 rot. nb. ind. fix. pt. Julia set. |
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| (hi res) |
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| 34/89 |
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| (hi res) |
Golden mean Siegel disk
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| Golden mean Siegel disk |
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| (hi res) |
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| Closeup on the critical point of the golden mean quadratic Siegel disk |
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| (hi res) |
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| Approx. domain of def. of the McMullen limit map |
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| (hi res) |
Quasiconformal models
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| Ghys model for the quad. gold. mean Sieg. disk. |
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| (hi res) |
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| Full Julia set of the previous Blaschke fraction. |
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| (hi res) |
Virtual Siegel disks
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| Virtual Siegel disk in the cauliflower |
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| (hi res, color) |
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| (lo res, grayscale) |
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| Siegel disk tending to the previous |
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| (hi res) |
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| Virtual Siegel disk in the 2/5 rabbit |
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| (hi res) |
Pérez-Marco's Riemann sufaces
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| Uniformization of Pérez-Marco's tube-log Riemann surface |
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| (hi res, color) |
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| (lo res, grayscale) |
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| (hi res, black and white) |
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| Uniformization of another Riemann surface of Pérez-Marco |
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| (hi res, color) |
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| (lo res, grayscale) |
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| (hi res, black and white) |
Siegel disk of exp(z)+c
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| The golden mean fixed Siegel disk in the family exp(z)+c (lo res, grayscale) |
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| (hi res, black and white) |
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| Plus some of its invariant circles (medium, color) |
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| (hi res, color) |
Digitated Siegel disk
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| Digitated Siegel disk |
Zakeri's Jordan curve
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| Zakeri's Jordan curve in a slice of the parameter space of cubic polynomials |
Pseudo hedgehogs
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| A pseudo hedgehog |
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| Another |
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| Another |
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| Another |
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| Another |
Near matings
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| Two mating polynomial Julia sets |
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| Close-up on the previous one |
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| Douady's rabbit mating with a dendrite |
Near tunings
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| Tuning a dragon by a segment |
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| ... closer to the limit |
A disconnected rational Julia set
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| A disconnected rational Julia set |
Bifucation loci in parameter spaces
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| Mandelbrot sets everywhere |
A Julia set equal to the Riemann sphere, looks like Jupiter's moon Callisto
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| 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.
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| Julia set with a Herman ring |
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| Same Julia set, shades of gray revealing more structure |
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| Another representation |
Parabolic renormalization
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| Shishikura's invariant class |
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| exp |
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| tan |