from numpy import cos, arctan
import numpy as np
import matplotlib.pyplot as plt

plt.rcParams["font.size"] = 10
plt.rcParams["mathtext.fontset"] = "cm"

x1, x2 = np.mgrid[-1.25:1.25:101j, -1.25:1.25:101j]
fun = x1*x2
cons = x1**2 + x2**2 - (1 + 0.2*cos(8*arctan(x1/x2)))**2
fun[cons > 0.01] = np.nan
levels = np.linspace(-1, 1, 30)
plt.contour(x1, x2, fun, levels, cmap="seismic")
plt.contour(x1, x2, cons, [0], colors="black")
plt.axis("image")
plt.xlabel(r"$x$", fontsize=14)
plt.ylabel(r"$y$", fontsize=14)
plt.savefig("simionescu's function.svg", bbox_inches="tight")
plt.show()