draw euclid norm illustration

euclid.py

import numpy as np
import matplotlib.pyplot as plt
x = np.linspace(-1, 1, 100)
x_r = np.linspace(1, -1, 100)
f_x = np.concatenate((x, x_r))
powers = [1, 2, 3, 4, 100]
label_str_list = ['$|x|+|y|=1$',
    '$x^2+y^2=1$',
    '$|x|^3+|y|^3=1$',
    '$x^4+y^4=1$',
    '$x^{100}+y^{100}=1$']
for j in range(5):
    i = powers[j]
    y = np.power(1-np.power(np.abs(x),i), 1.0/i)
    y_r = -1* np.power(1-np.power(np.abs(x),i), 1.0/i)
    f_y = np.concatenate((y, y_r))
    plt.plot(f_x, f_y, label=label_str_list[j])
plt.legend()
plt.savefig('euclid.png', transparent=True)
plt.show()