print'approaching brownian motion through limit of scaled random walk'importnumpyasnpmu,sigma=0,1# mean and standard deviationnmax=1000;s=np.random.normal(mu,sigma,nmax)#s = np.random.standard_cauchy(nmax)ss=np.cumsum(s)importmatplotlib.pyplotasplt@interactdeff(n=(1..nmax)):P=points([(i/n,1/sqrt(n)*ss[i+1])foriinrange(0,n)])P.set_axes_range(0,1,-2,2)show(P)
approaching brownian motion through limit of scaled random walk