Gallery

Planes in 3-manifolds


Tetrahedron Gallery
Acylindrical Gallery
Arithmetic and acylindrical
Acylindrical: Spherical view
Isolation phenomena

Nash embedding

Flat torus

Hilbert modular surfaces

Snow falling on cedars

Billiards

Pentgaon
Unfolding
Pentagons (Dance: Diana Davis)
Trapped
L-shaped reality (Duchin)
L-shaped table (Bowman)
Zero flux Peano curve
Saddle Connections
Polygon Flux
W44 (Mukamel)

Dynamics on P^2 and its blowups

Lattès examples on P^2
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)

Dynamics on K3 surfaces

*K3 movie
K3 surface
Tame
Wilder
Ergodic
Stable manifold
Droplets
Tame blowup
K3s in color
Poncelet's theorem
Poncelet Java (Schwartz)
Dynamics on a (2,2) curve
Dynamics on Fermat quartic

Curvature Flow

*Starfish - trace
*Matisse -
trace
Flying beetles (D. Gehktman)

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 (Joukowsky)
Streamlines
*Complex roots movie
|Zeta(s)| on s=1/2+it
Random QC map (Rohde)

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
PML (Dumas)
Animated slices (Dumas)
Holomorphic motion
Teichopsia

3-Manifolds


Not Knot (Geom Ctr)
Poincaré sphere (Jenn3D)
Celtic knot
Tait and Little's tables

Platonism

The 5 solids
Kepler's orbs
Golden rectangles
*Fibonacci Living Sculptures
*Icosahedron movie
Icosahedral dynamics
Poincaré recurrence
17 kinds of wallpaper

Fractional dimension

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

Topology

Plane filling foliation
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
Characteristic Manifold
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)

Kleinian movies

*Jellyfish movie
*Whitehead movie
*The Blob movie (Brock)
*Apollonian movie (Dumas)
*3D Kleinian Group (Rugh)

Mandelbrot set

Mandelbrot set
Mandelbrot ancient map (from here)
Mandelbrot catalog (Baez)
Hairiness of M
M near Fibonacci
M Obscura

Quadratic polynomials


M_1
Airplane
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
Bagel of Entropy (Koch)

Quadratic rational maps


0/1 Blaschke product
1/3 Blaschke product
Blaschke product - horocylic
Bifurcations
Bifurcations in a(z+1/z+t)
Bifurcations in Per_1(attr)
Bitransitive period 3
(cf. S3 Quartic)
Yin and Yang

Complex dynamics

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

Complex dynamics movies

Julia movie
Dancing Cantors movie
Mandelbrot zoom movie
Mandelbrot set tour
Mating (Buff)
Illegal Mating (Cheritat)
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

Number theory

Factorization (Schwartz)

Reality (mathematical)

Tasse de cafe (Wilkinson)

Copyright (c) 2015

Curtis T McMullen