Simulation of a Poisson Process

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

Note that the Poisson distribution therefore also describes the distribution of distances from one point to the next, assuming the points are distributed uniformly at random along a line, with average density Lambda per unit length.

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

**POISSON_SIMULATION** is available in
a C version and
a C++ version and
a FORTRAN90 version and
a MATLAB version.

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.

FAIR_DICE_SIMULATION, a MATLAB program which simulates N tosses of 2 dice, making a histogram of the results.

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.

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, a MATLAB program which simulates a random walk in a 3-dimensional region.

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.

- poisson_fixed_events.m, simulates the Poisson process until a fixed number of events have occurred.
- poisson_fixed_time.m, simulates the Poisson process until a fixed amount of time has passed.
- poisson_next_event.m, simulates the Poisson process until one event has occurred.
- timestamp.m, prints the YMDHMS date as a timestamp.