| 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() |