## Gallery

#### Planes in 3-manifolds

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

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
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

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
SL_2(Z[i])
Figure 8 orbifold fiber
Totally degenerate group
Griffin
Snowflake & blowup
Convex hull
Bubbles (Brock)

#### Kleinian movies

*Jellyfish 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

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)

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

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)