BROWNIAN_MOTION_SIMULATION
Simulation of Brownian Motion in M Dimensions

BROWNIAN_MOTION_SIMULATION is a Python library which simulates Brownian motion in an M-dimensional region.

Brownian motion is a physical phenomenon which can be observed, for instance, when a small particle is immersed in a liquid. The particle will move as though under the influence of random forces of varying direction and magnitude.

There is a mathematical idealization of this motion, and from there a computational discretization that allows us to simulate the successive positions of a particle undergoing Brownian motion.

Usage:

x = brownian_motion_simulation ( n, m, d, t )

• n is the number of time steps to take (default 1000);
• m is the spatial dimension, (default 2);
• d is the diffusion coefficient, (default 10.0);
• t is the total time interval (default 1.0);

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

BROWNIAN_MOTION_SIMULATON is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

DUEL_SIMULATION, a Python program which simulates N repetitions of a duel between two players, each of whom has a known firing accuracy.

SNAKES_AND_LADDERS, Python programs which simulate the game of Snakes and Ladders.

Source Code:

• brownian_motion_simulation.py, simulates Brownian motion.

Examples and Tests:

Some plots are made by the test program.

• motion_1d.png, a plot of a Brownian motion trajectory in 1D, with time as second dimension.
• motion_2d.png, a plot of a Brownian motion trajectory in 2D.
• motion_3d.png, a plot of a Brownian motion trajectory in 3D.
• displacement_1d.png, a plot of squared displacements, averaged over several 1D Brownian motions.
• displacement_2d.png, a plot of squared displacements, averaged over several 2D Brownian motions.
• displacement_3d.png, a plot of squared displacements, averaged over several 3D Brownian motions.

You can go up one level to the Python source codes.