Here is a simple example function which computes the value of pi by generating uniformly distributed points inside a square of side length 1 and determining the fraction of those points which fall inside the circle. Four times that fraction will be an approximation to pi.
function mypi = approxpi(n)
% Input: n = number of points to generate
% Default is n = 1e6
% Larger values of n should perform better
if nargin < 1
n = 1e6;
end
% Generate uniformly distributed points in
% [0, 1] x [0, 1]
xy = rand(n, 2);
% Compute distance from (0.5, 0.5)
r = sqrt((xy(:,1)-0.5).^2+(xy(:,2)-0.5).^2);
% Count fraction of points within 1/2 unit of (0.5, 0.5)
frac = sum(r <= 0.5) / n;
% Since square has side 1, circle has radius (1/2)
% and should have area of pi*(1/2)^2
% frac is approximately pi/4 so pi is approximately 4*frac
mypi = 4*frac;
Another example on Monte Carlo Simulation using MATLAB can be found at:
