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<html>
<head>
<title>
RANDOM_WALK_3D_SIMULATION - Simulation of a Random Walk in a 3D Region
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
RANDOM_WALK_3D_SIMULATION <br> Simulation of a Random Walk in a 3D Region
</h1>
<hr>
<p>
<b>RANDOM_WALK_3D_SIMULATION</b>
is a MATLAB program which
simulates a random walk in a 3D region.
</p>
<p>
The program <b>RANDOM_WALK_3D_SIMULATION</b> plots averaged data for
any number of random walks that each use the same number of steps.
The data plotted is the average and maximum of the distance squared
at each time step. The average distance squared should behave like
the number of time steps.
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<blockquote>
<b>random_walk_3d_simulation</b> ( <i>step_num</i>, <i>walk_num</i> )
</blockquote>
where
<ul>
<li>
<i>step_num</i> is the number of steps to take. 500 might be
a typical value.
</li>
<li>
<i>walk_num</i> is the number of random walks to take. The data
that is plotted comes from the average over all these walks.
</li>
</ul>
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>RANDOM_WALK_3D_SIMULATION</b> is available in
<a href = "../../m_src/random_walk_3d_simulation/random_walk_3d_simulation.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/brownian_motion_simulation/brownian_motion_simulation.html">
BROWNIAN_MOTION_SIMULATION</a>,
a MATLAB program which
simulates Brownian motion in an M-dimensional region.
</p>
<p>
<a href = "../../m_src/dice_simulation/dice_simulation.html">
DICE_SIMULATION</a>,
a MATLAB program which
simulates N tosses of M dice, making a histogram of the results.
</p>
<p>
<a href = "../../m_src/duel_simulation/duel_simulation.html">
DUEL_SIMULATION</a>,
a MATLAB program which
simulates N repetitions of a duel between two players, each of
whom has a known firing accuracy.
</p>
<p>
<a href = "../../c_src/forest_fire_simulation/forest_fire_simulation.html">
FOREST_FIRE_SIMULATION</a>,
a C program which
simulates the occurrence of fires and regrowth in a forest,
displaying the results using X Windows,
by Michael Creutz.
</p>
<p>
<a href = "../../m_src/gamblers_ruin_simulation/gamblers_ruin_simulation.html">
GAMBLERS_RUIN_SIMULATION</a>,
a MATLAB program which
simulates the game of gambler's ruin.
</p>
<p>
<a href = "../../m_src/high_card_simulation/high_card_simulation.html">
HIGH_CARD_SIMULATION</a>,
a MATLAB 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.
</p>
<p>
<a href = "../../m_src/ising_2d_simulation/ising_2d_simulation.html">
ISING_2D_SIMULATION</a>,
a MATLAB 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.
</p>
<p>
<a href = "../../c_src/life_opengl/life_opengl.html">
LIFE_OPENGL</a>,
a C program which
uses OpenGL to display the evolution of John Conway's "Game of Life",
by Simon Green.
</p>
<p>
<a href = "../../m_src/lorenz_simulation/lorenz_simulation.html">
LORENZ_SIMULATION</a>,
a MATLAB program which
solves the Lorenz equations and displays the solution, for various
starting conditions.
</p>
<p>
<a href = "../../f_src/md1/md1.html">
MD1</a>,
a FORTRAN90 program which
carries out a simple molecular dynamics simulation;
</p>
<p>
<a href = "../../f_src/md2/md2.html">
MD2</a>,
a FORTRAN90 program which
carries out a simple molecular dynamics simulation;
</p>
<p>
<a href = "../../f_src/md3/md3.html">
MD3</a>,
a FORTRAN90 program which
carries out a simple molecular dynamics simulation;
</p>
<p>
<a href = "../../f_src/md3glue/md3glue.html">
MD3GLUE</a>,
a FORTRAN90 program which
carries out a simple molecular dynamics simulation;
</p>
<p>
<a href = "../../m_src/poisson_simulation/poisson_simulation.html">
POISSON_SIMULATION</a>,
a MATLAB library which
simulates a Poisson process in which events randomly occur with an
average waiting time of Lambda.
</p>
<p>
<a href = "../../m_src/random_walk_1d_simulation/random_walk_1d_simulation.html">
RANDOM_WALK_1D_SIMULATION</a>,
a MATLAB program which
simulates a random walk in a 1-dimensional region.
</p>
<p>
<a href = "../../m_src/random_walk_2d_avoid_simulation/random_walk_2d_avoid_simulation.html">
RANDOM_WALK_2D_AVOID_SIMULATION</a>,
a MATLAB program which
simulates a self-avoiding random walk in a 2-dimensional region.
</p>
<p>
<a href = "../../m_src/random_walk_2d_simulation/random_walk_2d_simulation.html">
RANDOM_WALK_2D_SIMULATION</a>,
a MATLAB program which
simulates a random walk in a 2-dimensional region.
</p>
<p>
<a href = "../../m_src/reactor_simulation/reactor_simulation.html">
REACTOR_SIMULATION</a>,
a MATLAB 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."
</p>
<p>
<a href = "../../m_src/sir_simulation/sir_simulation.html">
SIR_SIMULATION</a>,
a MATLAB program which
simulates the spread of a disease through a hospital room of M by N beds,
using the SIR (Susceptible/Infected/Recovered) model.
</p>
<p>
<a href = "../../m_src/three_body_simulation/three_body_simulation.html">
THREE_BODY_SIMULATION</a>,
a MATLAB 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.
</p>
<p>
<a href = "../../m_src/traffic_simulation/traffic_simulation.html">
TRAFFIC_SIMULATION</a>,
a MATLAB program which
simulates the cars waiting to get through a traffic light.
</p>
<p>
<a href = "../../m_src/truel_simulation/truel_simulation.html">
TRUEL_SIMULATION</a>,
a MATLAB program which
simulates N repetitions of a duel between three players, each of
whom has a known firing accuracy.
</p>
<p>
<a href = "../../c_src/xising/xising.html">
XISING</a>,
a C program which
models the variations in ferromagnetism in a material, displaying
the results using X Windows.
</p>
<p>
<a href = "../../c_src/xwaves/xwaves.html">
XWAVES</a>,
a C program which
simulates the behavior of solutions of certain forms of the wave equation,
displaying the results using X Windows.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Martin Gardner,<br>
The Mathematical Circus,<br>
Mathematics Association of America, 1996,<br>
ISBN13: 978-0883855065,<br>
LC: QA95.G287.
</li>
<li>
Ian Stewart,<br>
"Repealing the Law of Averages",<br>
Scientific American,<br>
Volume 278, Number 4, April 1998, pages 102-104.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "random_walk_3d_simulation.m">random_walk_3d_simulation.m</a>,
the program that takes many walks and plots the averaged statistics.
</li>
<li>
<a href = "random_walk_3d_plot.m">random_walk_3d_plot.m</a>,
plots the trajectory of a 3D random walk.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "walk_1_steps_500.png">walk_1_steps_500.png</a>,
statistics for 1 walk of 500 steps.
</li>
<li>
<a href = "walk_10_steps_500.png">walk_10_steps_500.png</a>,
statistics for 10 walks of 500 steps.
</li>
<li>
<a href = "walk_100_steps_500.png">walk_100_steps_500.png</a>,
statistics for 100 walks of 500 steps.
</li>
<li>
<a href = "walk_1_steps_50000.png">walk_1_steps_50000.png</a>,
statistics for 1 walk of 50000 steps.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../m_src.html">
the MATLAB source codes</a>.
</p>
<hr>
<i>
Last revised on 06 November 2009.
</i>
<!-- John Burkardt -->
</body>
</html>