Gallery

Curvature Flow

Starfish
Melting Matisse
(original cutout)

Dynamics on blowups of P2

9 points : pencil of cubics
10: dynamics / cusp
11: dynamics / cusp
11: dynamics / conic+line
-- inverse dynamics /
11 points: Siegel disk
12: dynamics / three lines
Invariant smooth cubic
Stable/unstable manifolds
Conway's map (y,y-1/x)

Hyperbolic plane

Triangles and curvature
Octagons
Pentagons
Decagons
SL2 Z
Q/Z and unit disk
{{2,1},{1,1}} geodesic
Gamma(2)
Ideal triangles
Farey packing
Geodesics
Horoballs
SL2 Z lamination
Torus lamination
Open Riemann surface

Complex analysis

Hexponential for 31/3
Hexponential for 2E
Hexponential horocycle
Airfoils
Streamlines
Complex roots movie
|Zeta(s)| on s=1/2+it

Solving polynomials

Historical overview
Newton's method
Newton's bifurcations
Solving the cubic
Solving the quintic
Solving the sextic (Crass)

Teichmüller space

Maskit slice
Bers slice - square torus
Bers slice - hex torus
Anosov slice
Exotic slice
Animated slices (Dumas)
Holomorphic motion

Platonism

The 5 solids
Kepler's orbs
Golden rectangles
Icosahedron movie
Icosahedral dynamics
Poincaré recurrence

Fractional dimension

Random walks
Koch curve
Hironaka's M-curve
Riemann's curve
Diffusion limited aggregate
DJIA
Percolation
More percolation (Julia Fish)

Topology

Celtic knot
Bicycle tracks?
1881: Klein discovers ribbon graphs
Outer space

Kleinian groups

Sierpinski carpet limit set
Quasifuchsian reflections
Poincaré's discussion
Cusp group
Near cusp
Alg/Geom Limits
Honeycomb cusp
Apollonian gasket
Whitehead link
SL_2(Z[i])
Whitehead's carpet
Figure 8 orbifold fiber
Totally degenerate group
Griffin
Snowflake & blowup
Convex hull
Bubbles (Brock)
Not Knot (Geom Ctr)

Kleinian movies

Jellyfish movie
Whitehead movie
The Blob movie (Brock)
Apollonian movie (Dumas)

Quadratic polynomials

Mandelbrot set
M Obscura
M_1
Basilica (z2-1)
Rabbit
Tuned Rabbit
Tree (z2 + i)
Draped tree (à la Christo)
Lamination for z2 + i
Cusped curve (z2 + 1/4)
Nonstandard Parabolic (Cheritat)
Satellite
Cantor set and foliations

Quadratic rational maps


0/1 Blaschke product
1/3 Blaschke product
Bifuractions
Bifurcations in a(z+1/z+t)
Bitransitive period 3
(cf. S3 Quartic)
Yin and Yang

Complex dynamics

Sierpinski carpet Julia set
Cubic polynomial
Cubic rational map
Icosahedral maps
Deg 29 movie
Exponential map
Lattès Orbit (z-i)2/(z+i)2
Lightning (Hironaka)
Napoleon map and
Napoleonic bifurcations

Complex dynamics movies

Julia movie
Dancing Cantors movie
Mandelbrot zoom movie
Mating (Buff)
Vanishing limb movie

Renormalization

Cascade of bifurcations
Window of period 3
Small M in M
Colorful M in M
Feigenbaum Julia set
Golden Siegel disk
Golden circle map

Dynamics on K3 surfaces

K3 movie
K3 surface
Tame
Wilder
Ergodic
Stable manifold
Droplets
Tame blowup
Poncelet's theorem
Poncelet Java (Schwartz)
Dynamics on a (2,2) curve
Dynamics on Fermat quartic

Number theory

Factorization (Schwartz)

Billiards

Pentgaon
Unfolding
Trapped
L-shaped reality (Duchins)
Zero flux Peano curve
Copyright (c) 2006

Curtis T McMullen