![Zoom in on a fractal diffusion front in a bidimensional medium obtained by means of a random walk process [Zoom sur un front fractal de diffusion dans un milieu bidimensionnel obtenu grâce à un processus de marche aléatoire ]](image.jpg "Zoom in on a fractal diffusion front in a bidimensional medium obtained by means of a random walk process [Zoom sur un front fractal de diffusion dans un milieu bidimensionnel obtenu grâce à un processus de marche aléatoire ]")
Zoom in on a fractal diffusion front in a bidimensional medium obtained by means of a random walk process [Zoom sur un front fractal de diffusion dans un milieu bidimensionnel obtenu grâce à un processus de marche aléatoire].
Zoom in on a fractal diffusion front in a bidimensional medium obtained by means of a random walk process [Zoom sur un front fractal de diffusion dans un milieu bidimensionnel obtenu grâce à un processus de marche aléatoire].
(with constant concentration).
From time to time, each particle is free to move to one of its four first neighbour sites
-East, South, West and North- on the condition this site is free
(see a zoom in on the first steps of this process: 
).
After a long simulation time, five subsets can be defined:
the "Earth" (bright green) is the subset of particles 4-connected to the source,
the "Islands" (dark green) are the subsets of particles not 4-connected to the source,
the "Sea" (blue) is the subset of empty sites not surrended by the Earth,
the "Lakes" (cyan) are the subsets of empty sites not 8-connected to the Sea,
the "Shore" (yellow) is the the subset of the Earth close to the Sea.
The "Shore" is a fractal object with a dimension equals to 7/4.
