create a monte carlo simulation for pi in matlab

Here is an example code for a Monte Carlo simulation in MATLAB to estimate the value of pi:

main.m
N = 1000000; % number of random points
x = rand(N,1); % generate random x coordinates
y = rand(N,1); % generate random y coordinates
dist = sqrt(x.^2 + y.^2); % calculate distance from origin
points_in_circle = sum(dist<=1); % count number of points within unit circle
pi_estimated = 4*points_in_circle/N; % estimate pi
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Explanation: We first define the number of random points as N. Then we generate N random x and y coordinates between 0 and 1 using the rand() function. Next, we calculate the Euclidean distance of each point from the origin using the sqrt() function. We then count the number of points that lie within a unit circle centered at the origin by checking if the distance is less than or equal to 1. Finally, we estimate pi as four times the ratio of the number of points within the unit circle to the total number of points generated.

Note that the accuracy of the estimated value of pi depends on the number of random points generated.