percolation_simulation, a MATLAB code which simulates a percolation system. A rectangular region is decomposed into a grid of MxN squares. Each square may be porous or solid. We are interested in a path of porous squares connecting the top and bottom, or the left and right boundaries. The original MATLAB code was written by Ian Cooper.
Both percolation and diffusion consider systems in which mixing occurs. Diffusion tends to ignore spatial variations in system properties, and concentrates on transport over time due to random fluctuations in position. Percolation concerns properties of an underlying substrate, which may or may not be conducive to fluid transfer through randomly existing channels, or the existence of large connected voids.
Variations of the percolation model can be applied to oil and gas exploration, underground water flow, the transmission of rumors, the spread of a forest fire, the spatial progress of an epidemic, or the chances that an object made of a combination of transmitting and insulating metals will pass a current from one side to the other.
The computer code and data files described and made available on this web page are distributed under the MIT license
percolation_simulation is available in a MATLAB version and a Python version.
brownian_motion_simulation, a MATLAB code which simulates Brownian motion in an M-dimensional region.
bwlabel_test, a MATLAB code which calls bwlabel(), which is a built-in MATLAB function, which is given a binary matrix, and organizes the 1 values into labeled clusters, using 4-way or 8-way connectivity.
chuckaluck_simulation, a MATLAB code which simulates the Chuck-a-Luck gambling game.
clock_solitaire_simulation, a MATLAB code which simulates the game of clock solitaire. The deck is dealt into 13 piles of 4 cards each. Repeatedly, the top card a pile is removed, and its rank indicates the next pile to consider. Game continues until an empty pile is reached. The game is won if all piles are empty. The quantity of interest is the probability of winning.
coin_simulation, a MATLAB code which looks at ways of simulating or visualizing the results of many tosses of a fair or biased coin.
dice_simulation, a MATLAB code which simulates N tosses of M dice, making a histogram of the results.
duel_simulation, a MATLAB code which simulates N repetitions of a duel between two players, each of whom has a known firing accuracy.
fair_dice_simulation, a MATLAB code which simulates N tosses of 2 dice, making a histogram of the results.
fire_simulation, a MATLAB code which simulates a forest fire over a rectangular array of trees, starting at a single random location.
full_deck_simulation, a MATLAB code which simulates a process in which a random card is drawn from a deck of 52, and then replaced, continuing until every card has been seen at least once.
gamblers_ruin_simulation, a MATLAB code which simulates the game of gambler's ruin.
high_card_simulation, a MATLAB code which simulates a game in which you have one chance to select the highest card from a deck.
ising_2d_simulation, a MATLAB code 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.
jai_alai_simulation, a MATLAB code which simulates matches of jai alai.
poisson_simulation, a MATLAB code which simulates a Poisson process in which events randomly occur with an average waiting time of Lambda.
random_walk_1d_simulation, a MATLAB code which simulates a random walk in a 1-dimensional region.
random_walk_2d_avoid_simulation, a MATLAB code which simulates a self-avoiding random walk in a 2-dimensional region.
random_walk_2d_simulation, a MATLAB code which simulates a random walk in a 2-dimensional region.
random_walk_3d_simulation, a MATLAB code which simulates a random walk in a 3-dimensional region.
reactor_simulation, a MATLAB code which a simple Monte Carlo simulation of the shielding effect of a slab of a certain thickness in front of a neutron source. This code was provided as an example with the book "Numerical Methods and Software."
roulette_simulation, a MATLAB code which simulates the spinning of a roulette wheel and the evaluation of certain common roulette bets.
sir_simulation, a MATLAB code which simulates the spread of a disease through a hospital room of M by N beds, using the SIR (Susceptible/Infected/Recovered) model.
snakes_and_ladders_simulation, a MATLAB code which simulates the game of Snakes and Ladders.
traffic_simulation, a MATLAB code which simulates the cars waiting to get through a traffic light.
truel_simulation, a MATLAB code which simulates N repetitions of a duel between three players, each of whom has a known firing accuracy.
urn_simulation a MATLAB code which simulates an experiment in which k colored marbles are drawn from an urn containing a total of n marbles. The quantity of interest is the number of marbles of each color.
The original MATLAB code was written by Ian Cooper. Some modifications were made by John Burkardt.