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Simulation of random processes and mathematical images
(the pictures are in postscript or pdf)

You can use these drawings for your own publications/talks free of charges (attribution demanded, creative commons licence CC-BY). I am always pleased to see that these pictures are used, so if you don't mind telling me, with a short email for example...
If you desire a personal picture, you may also ask for it: if my program is not lost, it should be possible...

Uniform quadrangulations (the map structure is lost, only the underlying graph structure is kept.
Pictures in pdf :  size-150,   size 2500,   size 5000,    size 7500,   size 10 000,   size 20 000,   size 25 000a,   b,   c,   d,   e,   f,   g ,   size 30 000,   size 50 000
(size= number of vertices)

Uniform quadrangulations where separating cycles have been deleted 
Pictures in pdf. size-150 000,   size 150 000,   size 300 000,   size 400 000,   size 500 000,  
(size= number of vertices before deleting the separating cycles.)

Uniform planar trees (drawing style 1) size = number of nodes, pictures in pdf,  size 50,   size 100,   size 500,   size 1000,   size 5 000,   size 15 000

Uniform planar trees (drawing style 2)
size = number of nodes, pictures in pdf,  size 1000,   size 5 000,   size 10 000,   size 25 000,   size 50 000,   size 100 000

(combinatorial) minimum spanning tree of a complete graph
size = number of nodes, pictures in pdf,  size 1 000,   size 5 000,   size 10 000,   size 25 000,   size 50 000,   size 100 000

Diffusion limited aggregation (DLA)
size = number of particles, pictures in pdf or ps,  size 1 000,   size 5 000,   size 10 000,   size 50 000,   size 100 000,   size 500 000,   size 1 000 000

Internal DLA
The first step out of the cluster is drawn, giving a tree. Here, size = number of particles, pictures in ps,  size 1 000,   size 10 000,   size 100 000,   size 1 000 000

First passage percolation On the edges, i.i.d. uniform [0,1] random variables. Minimal paths to each vertex is drawn: again, this forms a tree.
size = temporal radius radius 10,   size 50 ,   size 100,   size 200

First passage percolation On the edges, i.i.d. uniform exponential random variables with parameter 1. Minimal paths to each vertex is drawn: again, this forms a tree.
size = temporal radius radius 10,   size 50 ,   size 100,   size 200

Sandpile models on the grid Z2 ("square") Put n grains at the origin of the square lattice Z2. When a vertex (i,j) has more than 4 grains, it is unstable, and then sends one grain to each neighbor (the neighbors are ((i+1,j), (i-1,j), (i,j+1),(i,j-1)). The process ends when all sites are stable.
nb of grains 10,   nb of grains 102    nb of grains 103    nb of grains 104    nb of grains 105    nb of grains 106    nb of grains 107 (large file 84 M) nb of grains 108 (huge file (500 M), be careful)

Sandpile models on the grid Z2 ("octogonal") Put n grains at the origin of the square lattice Z2. When a vertex (i,j) has more than 8 grains, it is unstable, and then sends one grain to each of its neighbors (i+a,j+b) for a,b not both zero, and a,b in {-1,0,+1}. The process ends when all sites are stable.
nb of grains 10,   nb of grains 102    nb of grains 103    nb of grains 104    nb of grains 105    nb of grains 106    nb of grains 107 (large file 46 M) nb of grains 108 (huge file (345 M), be careful)
Sandpile models on the grid Z2 ("hexagonal") Put n grains at the origin of the square lattice Z2. When a vertex (i,j) has more than 6 grains, it is unstable, and then sends one grain to each of its neighbors (i-1,j+1),(i,j+1),(i+1,j+1),(i-1,j-1),(i,j-1),(i+1,j+1) . The process ends when all sites are stable.
nb of grains 101    nb of grains 102    nb of grains 103    nb of grains 104    nb of grains 105    nb of grains 106    nb of grains 107 (large file 50 M)

Some processes(pictures in postscript)

Brownian motion 1 2 3
Brownian motion in R^2 1 2 3 4
Brownian bridge 1 2 3 4
Brownian excursion 1 2 3 4
Brownian meander 1 1 3 4
Uniform loop erased random walk (killed the first time at which 100 steps are present) 1 2 3 4
Uniform loop erased random walk (killed at 1 000 steps) 1 2 3 4
Uniform loop erased random walk (killed at 10 000 steps) 1 2 3 4
Uniform loop erased random walk (killed at 100 000 steps) 1 2 3 4
Uniform spanning tree: grid 50 x 50 1 2 3
Uniform spanning tree: grid 100 x 100 1 2 3
Uniform spanning tree: grid 200 x 200 1 2 3

Bessel processes with parameter   2   3   20   100   1000

Local times
Local time at time 1 of Brownian motion
Local time at time 1 of Brownian bridge
Local time at time 1 of the normalised Brownian excursion

Branching random walks
Discrete branching random walk (size 58 000) with positive mean displacment (and finite variance)
Discrete branching random walk (size 58 000) with gaussian spatial increments N(0,1).
Discrete branching random walk (size 58 000) with Cauchy spatial increments
Discrete branching random walk (size 180 000) with spatial increments distribution 5/(4(1+|x|)^7/2)

Brownian snakes
Brownian snake with lifetime the normalized Brownian excursion and R valued spatial process
Brownian snake with lifetime the normalized Brownian excursion and R2 valued spatial process
Random walk in random environment (critical: site uniform on [0.3,0.7], random walk +-1)
(Each site s received a random variable x(s) , uniform in [a,b], independent from the other sites: the walk at site s goes up with proba x(s) and down with proba 1-x(s) )
Random walk in random environment (critical: site uniform on [0.2,0.8], random walk +-1)
Random walk in random environment (site uniform on [0.2,0.9])

Quicksort limiting distribution
Density of limiting quicksort distribution (fix point of the law equality Y = U Y'+(1-U)Y''+2(U log(U)+(1-U) log(1-U)) +1, where Y' and Y'' are i.i.d. copies of Y, and are independent of U, uniform on [0,1]

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