random_walk_1d_simulation, an Octave 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.


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


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

Related Data and codes:


octave_simulation, an Octave 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.


  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:

Last revised on 18 November 2022.