import numpy as np
import matplotlib.pyplot as plt

def randMap(a, b, c):
    x = 1
    while True:
        x = (a*x + b) % c
        yield x

#xn1 = (a*xn + b) % c
#return xn1


N=1000 #number of iterations
#x = np.ones(N)

#Values from text book
a = 8121
b = 28411
c = 134456

#
randNum = randMap(a, b, c)

#Random ish points between 0-1 example

# x = np.ones(N)
# for i in range(1,N):
#     x[i] = next(randNum)
# x = x/c
# plt.plot(x[:(N-1)],x[1:N], 'o')
# plt.show()

#Random walkers
W = 10 #walker amount
t = range(N)

#random walks
for i in range(W):
    traj = np.zeros(N)
    pos = 0
    for j in range(1,N):
        if ((next(randNum)/c)>=0.5):
            pos +=1
        else:
            pos -=1
            #print('no')
        traj[j]=pos
    plt.plot(t, traj)

D = 0.5

sigma = np.sqrt(t)
plt.fill_between(t, 1.5*sigma, -1.5*sigma, facecolor = 'lavender')

#plt.style.use('dark_background')
plt.show()