Brownian motion really surprised me when I tried to simulate Stock market

save the following code in a Matlab file and run to see the graph.

clear all
x(1)=1;
sigma=0.1;
N=10000;
for t=1:N
  x(t+1)=x(t)+sigma*sign(2*rand-1);
  %x(t+1)=x(t)+randn*0.1;
endfor
plot(x);

Later I have found an article which says The brownian motion with power Laws is more practical.