DarkEnergy Flight:

import numpy as np
import matplotlib.pyplot as plt

# Define the parameters
c = 1.0
n = 2.0
φ0 = 0.5

# Define the function f(z)
def f(z):
    return c * np.abs(z)**n * (np.cos(n * np.angle(z)) + 1j * np.sin(n * np.angle(z)))

# Define the radius range
r_min = 0.0
r_max = 10.0
num_points = 100

# Create a list of radii
r_list = np.linspace(r_min, r_max, num_points)

# Calculate the scalar field values
phi_list = φ0 + c * np.abs(r_list)**n * np.cos(n * np.angle(r_list))

# Calculate the function f(r) values
f_r_list = f(r_list)

# Calculate the inverse of the function f(r) values
inv_f_r_list = 1 / f_r_list

# Plot the results
plt.figure(figsize=(10, 6))

plt.plot(r_list, phi_list, label=r"$\phi$", color="blue")
plt.plot(r_list, np.abs(f_r_list), label=r"|f(r)|", color="green")
plt.plot(r_list, np.real(f_r_list), label=r"Re[f(r)]", color="red")
plt.plot(r_list, np.imag(f_r_list), label=r"Im[f(r)]", color="purple")
plt.plot(r_list, inv_f_r_list, label=r"1/f(r)", color="black")

plt.xlabel(r"Radius (r)")
plt.ylabel(r"Value")
plt.title(r"Scalar field, function f(r), and its inverse")
plt.legend()

plt.grid(True)
plt.show()