# (c) Rory Clune 2/23/2011
# Random Walker with order Linear Congruential random number generator. Error bars derived analytically

from numpy import*
from pylab import*

rand = 1 #seed for random number generation
points = 1000 #number of random steps that will be taken
walkers = 1
x = zeros([1000])
for i in range (0,walkers):
    for j in range (1,points):    
        #Generate the next random number (linear congruential) in the range [1, 134456]
		rand = ((8121*rand + 28411)%134456)
		if rand < (134456/2):
			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()
print x