import numpy as np
import matplotlib.pyplot as plt

A = np.array([[[0.,0.],[0.,0.16]],
              [[0.85,0.04],[-0.04,0.85]],
              [[0.20,-0.26],[0.23,0.22]],
              [[-0.15,0.28],[0.26,0.24]]])
    
B = np.array([[0.,0.],
              [0.,1.60],
              [0.,1.60],
              [0.,0.44]])

ntrials = 40000
pos = np.zeros((ntrials,2))
for n in range(1,ntrials):
    type = np.random.choice(range(4),p=[0.01,0.85,0.07,0.07])
    pos[n] = A[type].dot(pos[n-1])+B[type]

plt.figure(figsize=(8, 12), dpi=80)
plt.scatter(pos[:,0],pos[:,1],c=pos[:,1]*0.5,alpha=0.5,s=10,marker='.')
plt.show()