Simulation of Brownian Motion in M Dimensions

BROWNIAN_MOTION_SIMULATION is a FORTRAN77 library which simulates Brownian motion in an M-dimensional region, creating graphics files for processing by gnuplot.

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.


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


BROWNIAN_MOTION_SIMULATON is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

CORRELATION, a FORTRAN77 library which contains examples of statistical correlation functions.

DUEL_SIMULATION, a FORTRAN77 program which simulates N repetitions of a duel between two players, each of whom has a known firing accuracy.

FAIR_DICE_SIMULATION, a FORTRAN77 program which simulates N tosses of 2 dice, making a histogram of the results.

GNUPLOT, FORTRAN77 programs which illustrate how a program can write data and command files so that gnuplot can create plots of the program results.

HIGH_CARD_SIMULATION, a FORTRAN77 program which simulates a situation in which you see the cards in a deck one by one, and must select the one you think is the highest and stop; the program uses GNUPLOT for graphics.

ISING_2D_SIMULATION, a FORTRAN77 program which carries out a Monte Carlo simulation of an Ising model. a 2D array of positive and negative charges, each of which is likely to flip to be in agreement with neighbors.

POISSON_SIMULATION, a FORTRAN77 library which simulates a Poisson process in which events randomly occur with an average waiting time of Lambda.

REACTOR_SIMULATION, a FORTRAN77 program which a simple Monte Carlo simulation of the shielding effect of a slab of a certain thickness in front of a neutron source. This program was provided as an example with the book "Numerical Methods and Software."

THREE_BODY_SIMULATION, a FORTRAN77 program which simulates the behavior of three planets, constrained to lie in a plane, and moving under the influence of gravity, by Walter Gander and Jiri Hrebicek.

Source Code:

Examples and Tests:

Some data files and plots are made by the test program.

You can go up one level to the FORTRAN77 source codes.

Last revised on 30 September 2012.