random_walk_1d_simulation

random_walk_1d_simulation, a Python code which simulates a random walk in a 1D region.

random_walk_1d_plot() plots the trajectories of one or more random walks. The plot becomes unreadable after 10 or 20 such trajectories.

random_walk_1d_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.

Licensing:

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

Languages:

random_walk_1d_simulation is available in a MATLAB version and an Octave version and a Python version.

Related Data and codes:

random_walk_1d_simulation_test

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_1d_simulation.py, the source code.
• random_walk_1d_simulation.sh, runs all the tests.
• random_walk_1d_simulation.txt, the output file.

• walk_1_steps_500.png, statistics for 1 walk of 500 steps.
• walk_10_steps_500.png, statistics for 10 walks of 500 steps.
• walk_100_steps_500.png, statistics for 100 walks of 500 steps.
• walk_5_steps_500_plot.png, the trajectories of 5 walks of 500 steps.
• random_walkers_1d.png, where 100 drunken sailors are after 120 random steps each.