RANDOM_WALK_3D_SIMULATION
Simulation of a Random Walk in a 3D Region


RANDOM_WALK_3D_SIMULATION, a MATLAB program which simulates a random walk in a 3D region.

The program RANDOM_WALK_3D_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_3d_simulation ( step_num, walk_num )
where

Licensing:

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

Languages:

RANDOM_WALK_3D_SIMULATION is available in a MATLAB version.

Related Data and Programs:

BROWNIAN_MOTION_SIMULATION, a MATLAB program which simulates Brownian motion in an M-dimensional region.

COIN_SIMULATION, a MATLAB library which looks at ways of simulating or visualizing the results of many tosses of a fair or biased coin.

DICE_SIMULATION, a MATLAB program which simulates N tosses of M dice, making a histogram of the results.

DUEL_SIMULATION, a MATLAB program which simulates N repetitions of a duel between two players, each of whom has a known firing accuracy.

GAMBLERS_RUIN_SIMULATION, a MATLAB program which simulates the game of gambler's ruin.

HIGH_CARD_SIMULATION, 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.

ISING_2D_SIMULATION, 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.

LIGHTS_OUT, a MATLAB program which sets up the "Lights Out" game and allows a user to try to solve it.

LORENZ_SIMULATION, a MATLAB program which solves the Lorenz equations and displays the solution, for various starting conditions.

POISSON_SIMULATION, a MATLAB library which simulates a Poisson process in which events randomly occur with an average waiting time of Lambda.

RANDOM_WALK_1D_SIMULATION, a MATLAB program which simulates a random walk in a 1-dimensional region.

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

RANDOM_WALK_2D_SIMULATION, a MATLAB program which simulates a random walk in a 2-dimensional region.

random_walk_3d_simulation_test

REACTOR_SIMULATION, 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."

ROULETTE_SIMULATION, a MATLAB program which simulates the spinning of a roulette wheel and the evaluation of certain common roulette bets.

SIR_SIMULATION, 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.

THREE_BODY_SIMULATION, 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.

TRAFFIC_SIMULATION, a MATLAB program which simulates the cars waiting to get through a traffic light.

TRUEL_SIMULATION, a MATLAB program which simulates N repetitions of a duel between three players, each of whom has a known firing accuracy.

XISING, a C program which models the variations in ferromagnetism in a material, displaying the results using X Windows.

XWAVES, a C program which simulates the behavior of solutions of certain forms of the wave equation, displaying the results using X Windows.

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:


Last revised on 11 March 2019.