brownian_motion_simulation

brownian_motion_simulation, an Octave code 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 MIT license

Languages:

brownian_motion_simulation is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

Related Data and codes:

brownian_motion_simulation_test

octave_simulation, an Octave code which use simulation to study card games, contests, and other processes which have a random element. Usually, the purpose is to try to predict the average behavior of the system over many trials.

Source Code:

• brownian_motion_simulation.m, simulates Brownian motion.
• brownian_motion_display.m, plots a Brownian motion trajectory for the case M = 2.
• brownian_displacement_simulation.m, computes the squared displacement over time, for an ensemble of cases.
• brownian_displacement_display.m, plots Brownian motion displacement versus the expected behavior for an ensemble of cases.