bioenthalpy5.py

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from matplotlib.animation import FuncAnimation
from matplotlib.widgets import Slider

# Define the 3D wavefunction in spherical coordinates
def wavefunction(theta, phi, r, k_theta, k_phi, k_r, omega, t):
    return np.exp(1j * (k_theta * theta + k_phi * phi + k_r * r - omega * t))

# Define parameters
k_theta, k_phi, k_r = 1.0, 1.0, 1.0
omega = 1.0

# Create the figure and slider axes
fig = plt.figure(figsize=(12, 10))
ax = fig.add_subplot(111, projection='3d')
slider_ax = plt.axes([0.2, 0.02, 0.6, 0.03])  # Slider position (left, bottom, width, height)

# Initialize the slider for controlling the number of displayed data points
num_points_slider = Slider(slider_ax, 'Points', valmin=10, valmax=30, valinit=30, valstep=1)

# Animation update function
def update(frame):
    ax.clear()

    # Adjust the number of points based on slider value
    num_points = int(num_points_slider.val)
    theta = np.linspace(0, 2 * np.pi, num_points)
    phi = np.linspace(0, 2 * np.pi, num_points)
    r = np.linspace(0.5, 5.0, num_points)
    Theta, Phi, R = np.meshgrid(theta, phi, r)

    # Convert to Cartesian coordinates for visualization
    X = R * np.cos(Phi) * np.sin(Theta)
    Y = R * np.sin(Phi) * np.sin(Theta)
    Z = R * np.cos(Theta)

    # Compute the wavefunction and density matrix
    t = frame / 20000.0  # Speed increased by a factor of 20,000x
    Psi = wavefunction(Theta, Phi, R, k_theta, k_phi, k_r, omega, t)
    rho = np.abs(Psi)**2  # Density matrix (real values)

    # Compute entropy (S) and bio-enthalpy (H_B)
    S = -rho * np.log(rho + 1e-9)  # Adding a small term to avoid log(0)
    H_B = rho + np.abs(np.gradient(Psi.real)[0])**2 + np.abs(np.gradient(Psi.real)[1])**2 + np.abs(np.gradient(Psi.real)[2])**2

    # Normalize S and H_B for visualization purposes
    S_normalized = S / np.max(S)
    H_B_normalized = H_B / np.max(H_B)

    # Plot entropy and bio-enthalpy together using color mapping
    scatter_entropy = ax.scatter(
        X.flatten(), Y.flatten(), Z.flatten(),
        c=S_normalized.flatten(), cmap='twilight', alpha=0.6,
        label="Entropy"
    )

    scatter_enthalpy = ax.scatter(
        X.flatten(), Y.flatten(), Z.flatten(),
        c=H_B_normalized.flatten(), cmap='hsv', alpha=0.4,
        label="Bio-Enthalpy"
    )

#     # Add vector arrows (gradient of Psi) - COMMENTED OUT
#     # ax.quiver(
#     #     X[::3].flatten(), Y[::3].flatten(), Z[::3].flatten(),
#     #     grad_Psi_x[::3].flatten(), grad_Psi_y[::3].flatten(), grad_Psi_z[::3].flatten(),
#     #     length=0.5, normalize=True,
#     #     color="blue", alpha=0.7,
#     #     label="Gradient Arrows"
#     # )

    # Add titles and labels
    ax.set_title(f'Entropy vs Bio-Enthalpy at t={t:.6f}')
    ax.set_xlabel('X')
    ax.set_ylabel('Y')
    ax.set_zlabel('Z')

# Load and animate the first 10 seconds with increased speed
def load_and_animate(duration=10, fps=30):
    frames = int(fps * duration)  # Total number of frames

    ani = FuncAnimation(fig, update, frames=frames, interval=1000 / fps)  # Interval in milliseconds
    plt.show()

# Connect slider interaction to update function
def slider_update(val):
    update(0)  # Update with initial time t=0 to reflect new slider value

num_points_slider.on_changed(slider_update)

# Run animation with interactive controls
load_and_animate(duration=10)