# RANDOM_WALK_2D_AVOID_SIMULATION Simulation of a Self-Avoiding Random Walk in a 2D Region

RANDOM_WALK_2D_AVOID_SIMULATION, a MATLAB program which simulates a self-avoiding random walk in a 2D region.

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".

The program RANDOM_WALK_2D_AVOID_PLOT 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.

The program RANDOM_WALK_2D_AVOID_SIMULATION 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.

### Usage:

random_walk_2d_avoid_plot ( step_num, walk_num )
where
• step_num is the number of steps to take. 100 might be a typical value.
• walk_num is the number of random walks to take. Each walk is plotted separately.

random_walk_2d_avoid_simulation ( step_num, walk_num )
where
• step_num is the number of steps to take. 100 might be a typical value.
• walk_num 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.

### Languages:

RANDOM_WALK_2D_AVOID_SIMULATION is available in a MATLAB version.

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### Reference:

1. Brian Hayes,
How To Avoid Yourself,
American Scientist,
Volume 86, Number 4, July-August 1998, pages 314-319.

### Source Code:

Last revised on 10 March 2019.