# (c) Rory Clune 2/23/2011
# Random Walker with order 34 LFSR random number generator. Taps at 1, 2, 27, 34
# Error bars derived analytically using solution of the diffusion equation by Fourier transforms

from numpy import*
from pylab import*

order = 34
rand = ones([order+1])
points = 1000
walkers = 10
x = zeros([1000])
for i in range (0,walkers):
    for j in range (1,points):    
        rand[0]=(rand[1]+rand[2]+rand[27]+rand[34])%2
        rand[1:order+1] = rand[0:order]
        if rand[0] == 0:
            x[j]=x[j-1]+1
        else:
            x[j]=x[j-1]-1 
    plot(x)

t = arange(0,points,(points/5))
error = 1.5*sqrt(t)
errorbar(t, zeros([size(t)]), yerr=error, fmt=None, ecolor = 'k')
axis([0,points,-150,150])
show()