# BROWNIAN_MOTION_SIMULATION Simulation of Brownian Motion in M Dimensions

BROWNIAN_MOTION_SIMULATION is a MATLAB 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 )
where
• 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.

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### Source Code:

Last revised on 04 December 2018.