Henon_attractor_BCD

import matplotlib.pyplot as plt
import scipy.optimize as opt
import numpy as np

n = 100000
m = 7
e0 = 1/2
a,b = 1.4, 0.3
x,y = 0,0
for i in range(1,201):
    x,y = a-x**2+b*y,x
S = []
for j in range(n):
    x,y = a-x**2+b*y,x
    xj,yj = x,y
    S.append((xj,yj))
S1 = np.array(S)      
evals = []
Nvals = []
for k in range(1,m+1):
    e = e0**k
    S2 = np.floor(S1/e)
    S3 = [tuple(l) for l in S2.tolist()]
    N = len(list(set(S3)))
    print(e, N)
    evals.append(log(1/e))
    Nvals.append(log(N))
evals2 = np.array(evals)
Nvals2 = np.array(Nvals)

matrix = np.vstack([evals2, np.ones(len(evals2))]).T

D, C = np.linalg.lstsq(matrix, Nvals2, rcond=None)[0]

print('The estimated value of the box-counting dimension is D =', D)

plt.plot(evals2, Nvals2, "bo", label="Data")
plt.plot(evals2, D*evals2 + C, 'r', label='Fitted line')
plt.title("Plot of ln N(epsilon) against ln(1/epsilon) with least-squares fit")
plt.legend(loc="upper left")