This document provides instructions for calculating pi using the Monte Carlo method in MATLAB. It describes generating random points within a circle of radius 1, counting the total number of points and number inside the circle, and using those values to calculate an approximate value of pi. The code provided generates random points on a plot in real time, displays a running count, and stops when the user clicks a toggle button. It outputs the approximate value of pi based on the random point counts.

1. MATLAB SIMULATION (SAMPLE ASSIGNMENT)
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Monte Carlo Method
This sample assignment shows Calculating pi using Monte Carlo Method
MonteCarlo.m
% To calculate the value of pi using Monte Carlo Method
%-------------------------------------------------------------------------
% Code written by : Siva Srinivas Kolukula |
% Senior Research Fellow |
% Structural Mechanics Laboratory |
% Indira Gandhi Center for Atomic Research |
% India |
% E-mail : allwayzitzme@gmail.com |
% http://sites.google.com/site/kolukulasivasrinivas/ |
%-------------------------------------------------------------------------
clear all ;clc ;
% Radius of the Circle
R = 1 ;
shg
clf reset
set(gcf,'color','w','menubar','none','numbertitle','off','name','Monte Carlo Method ') ;
x = [0.; 0.];
h = plot(x(1),x(2),'.');
set(h,'markersize',1.5,'erasemode','none');
title('Calculation of pi using Monte Carlo Method','Color','r','fontweight','bold') ;
axis([-R R -R R]) ;
axis equal ;
axis off ;
% Stop and close toggle button
stop = uicontrol('style','toggle','string','stop','position',[115,20,40,20],.....
'background','white');
% Text boxes
tb1 = uicontrol('style','text','position',[190 20 100 20],'background','w') ;
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2. tb2 = uicontrol('style','text','position',[320 20 150 20],'background','w') ;
drawnow ;
%
cnt = 1; % Count for Total Random Numbers
ccnt = 1 ; % Count for Random Numbers which lie inside circle
tic
while ~get(stop,'value')
% Generate Random Numbers between R and -R
x = 2*R*rand(2,1)-R ;
set(h,'XData',x(1),'YData',x(2),'Color','b') ;
drawnow
cnt = cnt + 1;
N = sprintf('N = %8.0f',cnt) ; % Update the total number of Random Numbers
set(tb1,'String',N)
RR = (x(1)^2+x(2)^2) ;
if RR<R^2 % If point lies inside the Circle
set(h,'XData',x(1),'YData',x(2),'Color','r') ;
drawnow ;
kssv = 4*ccnt/cnt ;
Pi = sprintf('pi(approx)=%6.8f',kssv) ; % Values of pi approximately
set(tb2,'String',Pi) ;
ccnt = ccnt+1 ;
end
end
toc
% Close the figure window
set(stop,'style','pushbutton','string','close','callback','close(gcf)')
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