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<html>
<head>
<title>
RANDOM_WALK_2D_AVOID_SIMULATION - Simulation of a Self-Avoiding Random Walk in a 2D Region
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
RANDOM_WALK_2D_AVOID_SIMULATION <br> Simulation of a Self-Avoiding Random Walk in a 2D Region
</h1>
<hr>
<p>
<b>RANDOM_WALK_2D_AVOID_SIMULATION</b>
is a MATLAB program which
simulates a self-avoiding random walk in a 2D region.
</p>
<p>
A random self-avoiding walk of length STEP_NUM in 2D can be generated
by generating a random walk in 2D and "hoping" it doesn't intersect itself.
If the next step would cause an intersection, then the generation is terminated
prematurely; to ensure that the self-avoiding random walks are selected uniformly,
we have to just keep trying random walks this way and "hoping".
</p>
<p>
The program <b>RANDOM_WALK_2D_AVOID_PLOT</b> plots the trajectories of one
or more self-avoiding random walks. The user gives a desired length STEP_NUM,
and the program generates a random walk that either reaches STEP_NUM without
self-intersection, or is terminated early to avoid intersection.
</p>
<p>
The program <b>RANDOM_WALK_2D_AVOID_SIMULATION</b> plots averaged data for
any number of self-avoiding random walks that each try to achieve
the same number of steps. The data plotted includes the number of steps
each walk reached before termination, and a least squares fit to the
distance versus number of steps.
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<blockquote>
<b>random_walk_2d_avoid_plot</b> ( <i>step_num</i> )
</blockquote>
where
<ul>
<li>
<i>step_num</i> is the number of steps to take. 100 might be
a typical value.
</li>
</ul>
After the walk is plotted, the user can hit RETURN to seek another
walk of the same length, which will be plotted together with the
previous walks.
</p>
<p>
<blockquote>
<b>random_walk_2d_avoid_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. 100 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.
100 might be a reasonable value to try.
</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_2D_AVOID_SIMULATION</b> is available in
<a href = "../../m_src/random_walk_2d_avoid_simulation/random_walk_2d_avoid_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_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/random_walk_3d_simulation/random_walk_3d_simulation.html">
RANDOM_WALK_3D_SIMULATION</a>,
a MATLAB program which
simulates a random walk in a 3-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>
Brian Hayes,<br>
How To Avoid Yourself,<br>
American Scientist,<br>
Volume 86, Number 4, July-August 1998, pages 314-319.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "random_walk_2d_avoid_simulation.m">random_walk_2d_avoid_simulation.m</a>,
the program that takes many walks and plots the averaged statistics.
</li>
<li>
<a href = "random_walk_2d_avoid_plot.m">random_walk_2d_avoid_plot.m</a>,
the program that takes one or more walks and plots the trajectories.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "avoid_2d_length_056.png">avoid_2d_length_056.png</a>,
the plot of a self-avoiding random walk, which was requested to be
of length 100, but which terminated at length 56.
</li>
<li>
<a href = "avoid_2d_length_100.png">avoid_2d_length_100.png</a>,
the plot of a self-avoiding random walk of 100 steps.
</li>
<li>
<a href = "count_100_100.png">count_100_100.png</a>,
a plot of how many random walks of a given length were found
when 100 such walks of length 100 were requested.
</li>
<li>
<a href = "fit_100_100.png">fit_100_100.png</a>,
a plot of a least squares fit log(D^2) = A * log(N) + B to the
data computed by random_walk_2d_avoid_simulation.
</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 10 November 2009.
</i>
<!-- John Burkardt -->
</body>
</html>