random_walk_2d_simulation

random_walk_2d_simulation, a Python code which simulates a random walk in a 2D region.

random_walk_2d_plot() plots the trajectories of one or more random walks.

random_walk_2d_simulation() 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.

Usage:

random_walk_2d_plot ( step_num, walk_num )

• step_num is the number of steps to take. 500 might be a typical value.
• walk_num is the number of random walks to take. Each walk is displayed on a common grid.

random_walk_2d_simulation ( step_num, walk_num )

• step_num is the number of steps to take. 500 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.

Licensing:

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

Languages:

random_walk_2d_simulation is available in a MATLAB version and an Octave version and a Python version.

Related Data and codes:

python_simulation, a Python code which uses 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.

Reference:

1. Martin Gardner,
   The Mathematical Circus,
   Mathematics Association of America, 1996,
   ISBN13: 978-0883855065,
   LC: QA95.G287.
2. Ian Stewart,
   "Repealing the Law of Averages",
   Scientific American,
   Volume 278, Number 4, April 1998, pages 102-104.

Source Code:

• random_walk_2d_simulation.py, the source code.
• random_walk_2d_simulation.sh, runs all the tests.
• random_walk_2d_simulation.txt, the output file.

• walks_1_steps_500_stats.png, statistics for 1 walk of 500 steps.
• walks_10_steps_500.png, statistics for 10 walks of 500 steps.
• walks_100_steps_500.png, statistics for 100 walks of 500 steps.
• walks_1_steps_10_plot.png, the trajectories of 1 walk of 10 steps.
• walks_1_steps_100_plot.png, the trajectories of 1 walk of 100 steps.
• walks_1_steps_1000_plot.png, the trajectories of 1 walk of 1000 steps.
• walks_1_steps_10000_plot.png, the trajectories of 1 walk of 10000 steps.
• walks_20_steps_100_plot.png, the trajectories of 20 walks of 100 steps.