Beautiful Eigenvalue Cloud

eigenvalue_cloud.py

import numpy as np
import matplotlib.pyplot as plt
import itertools
%matplotlib inline

lim = 20
n_points = 100000
t1 = np.linspace(-lim, lim, int(np.sqrt(n_points)))
t2 = np.linspace(-lim, lim, int(np.sqrt(n_points)))

all_eigenvalues = []

for (t1i, t2i) in itertools.product(t1,t2):
    raw = """
    -i -i  i  0 -i  0 -i;
    -i  0 .3 -i  0  0 -i;
     0 -i  0 .3  i .3  i;
     0 -i  i -i  i .3 -i;
     0  i  i  0  0 -i  i;
     0 .3  0 -i  0 {t1} 0;
    -i {t2} i i  i .3 -i
    """.format(t1 = t1i, t2 = t2i).replace("i","1j")

    matrix = np.mat(raw)
    eigenvalues, _ = np.linalg.eig(matrix)
    all_eigenvalues.append(eigenvalues)
    
final_eigenvalues = np.concatenate(all_eigenvalues)

plt.figure(figsize = (20,20))
plt.scatter(
    final_eigenvalues.real, 
    final_eigenvalues.imag, 
    marker = '.', color = 'k', alpha = 0.05, s=1)
plt.axes().set_aspect('equal')
plt.xlim([-3,3])