% BROWN  Script which shows a cloud of n particles undergoing Brownian 
% motion.  The motion is simulated by a random walk with normally distributed
% steps of mean size dx.  Note n and dx can be adjusted for better viewing.
% ELB 4/10/05

n = 100;  % number of particles
dx = 0.006;  % distance moved in one step
maxsteps = 100000;

dt=dx^2;  % scaling law for Brownian motion
x = zeros(n,1);  y = zeros(n,1);  % all particles start at origin

figure(1),  h = plot(x,y,'.');  title('Brownian particles')
text(-0.8,0.95,'stops when one leaves box (also: Ctrl-C stops)')
axis([-1 1 -1 1]), axis square, grid off
set(h,'EraseMode','xor','MarkerSize',18)  % makes previous dots disappear

for k=1:maxsteps 
   if ~all((x>-1)&(x<1)&(y>-1)&(y<1)), break, end
   x = x + dx*randn(n,1);  y = y + dx*randn(n,1);  % new positions
   set(h,'XData',x,'YData',y),  drawnow  % draw new positions
end
disp(['time for first particle to leave box = ' num2str(k*dt)])
disp(['      (number of steps of simulation = ' num2str(k) ')'])