# Required imports for plotting and numerical operations
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.colors import LogNorm
from mpl_toolkits.mplot3d import Axes3D

# Define the physical constants for our hypothetical fractal equation
c = 3e8 # Speed of light
G = 6.67e-11 # Gravitational constant
h = 6.626e-34 # Planck's constant
e = 1.602e-19 # Elementary charge

# Placeholder for unknown variables
X1 = 1.0
X2 = 1.0

# Fractal generating function inspired by Perelman's Ricci Flow and fundamental constants
def fractal_function(x, y, iteration):
z = x + 1j * y
c = z
for i in range(iteration):
R = np.abs(z)
theta = np.angle(z)
z = z**2 + c # Mandelbrot set equation as the core
z += c * h * G * X1 # Adding in our constants and unknowns to modulate the fractal
return z

# Coordinate setup with higher resolution
x = np.linspace(-2, 2, 1000)
y = np.linspace(-2, 2, 1000)
X, Y = np.meshgrid(x, y)

# Generate the fractal using fewer iterations for computational efficiency
Z = fractal_function(X, Y, 50)

# Create a larger 3D plot for Real and Imaginary parts
fig = plt.figure(figsize=(18, 9))
ax1 = fig.add_subplot(121, projection='3d')
ax2 = fig.add_subplot(122, projection='3d')

# Plot the real part with a gradient color map
surf1 = ax1.plot_surface(X, Y, Z.real, cmap="viridis", edgecolor='k')
ax1.set_title('Real Part')
fig.colorbar(surf1, ax=ax1, orientation='horizontal')

# Plot the imaginary part with a different gradient color map
surf2 = ax2.plot_surface(X, Y, Z.imag, cmap="inferno", edgecolor='k')
ax2.set_title('Imaginary Part')
fig.colorbar(surf2, ax=ax2, orientation='horizontal')

plt.show()