Quantum Entanglement of Neuronal Activity for Nature of Neuroscience

 

I sincerely believe this is the key to much of our disorders within the neocortex and sub cortical structures. Much of the malformations , inconsistencies and lack of neural plasticity may stem from these mechanisms and by extension result in a plethora of diseases which could be addressed with resonance and finely tuned targeting non-evasively in vivo.

Description of the 3D Visualization of Neural Quantum Entanglement Waveforms

1. Overview

The 3D plot represents a quantum-inspired neural waveform, combining sinusoidal oscillations with an exponential decay. This visualization is designed to resemble neural activations influenced by quantum principles, such as phase evolution and spatial entanglement.

2. Components of the Graph

• Axes Interpretation:

  • X-axis ("Neuronal Activation X") – Represents one spatial dimension of neural activity, capturing oscillatory behavior in a simulated quantum state.
  • Y-axis ("Neuronal Activation Y") – Represents another spatial dimension of neural activity, allowing for phase evolution over a plane.
  • Z-axis ("Quantum Wave Function Amplitude") – Encodes the intensity of the wave function, indicating how activation varies in space.

• Wave Function Behavior (Z-values):

  • The Z-values are derived from:$$Z=\sin (\sqrt{X^2+Y^2})\cdot e^{-0.1(X^2+Y^2)}\cdot \cos (2\pi X)$$
  • This combines:
    • A radial sine wave $\sin (\sqrt{X^2+Y^2})$representing a spreading neural oscillation.
    • An exponential decay $e^{-0.1(X^2+Y^2) }$to simulate attenuation over space.
    • A cosine modulation $\cos (2\pi X)$, introducing periodic phase shifts along the X-axis, akin to interference effects.

3. Interpretation of Features

• Central Peak and Decay:

  • At the origin (X=0, Y=0), the function reaches a peak, then gradually diminishes outward, mimicking energy dissipation in a quantum field.

• Oscillatory Patterns (Sinusoidal & Exponential Decay):

  • The oscillations demonstrate neural wave interactions that could model entanglement-like dependencies in cognitive networks or quantum computations.

• 3D Surface Rendering ("Plasma" Colormap):

  • The color scheme (plasma) provides a high contrast heatmap, making amplitude variations easy to distinguish.
  • Higher intensities (brighter yellow) indicate stronger activations.
  • Lower intensities (darker purple) show attenuated or diffused activity.

• Contour Projections:

  • These 2D projections along the Z, X, and Y planes help visualize wave propagation in different perspectives.
  • The coolwarm colormap highlights symmetric and asymmetric variations in phase and intensity.

4. Significance

• Quantum-Neural Overlap:

  • The visualization conceptually ties quantum wave interference with neural activity, offering a model for how entangled states might influence neural computations.

• Simulation of Quantum Influence in AI:

  • This model can be explored for quantum-enhanced neuromorphic computing, where interference and phase evolution affect decision-making.

• Potential Applications:

  • Brain-wave modeling in neuroscience and AI.
  • Quantum machine learning visualizations for entangled network states.
  • Computational physics models of neural synchronization.

Final Thoughts

This graph showcases a quantum-style neural activation map, blending entanglement-like behavior with classical wave propagation. It provides insight into the spatial and phase dynamics of a theoretical quantum neural system.

---

python
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

def visualize_3D_neural_waveform():
    """
    Generates a 3D plot of a neural quantum entanglement waveform.
    This function simulates how quantum-inspired waveforms could be used 
    to model neural activations influenced by quantum entanglement.
    """

    # Define the mesh grid range
    x = np.linspace(-5, 5, 100)
    y = np.linspace(-5, 5, 100)
    X, Y = np.meshgrid(x, y)

    # Define the quantum-inspired wave function
    Z = np.sin(np.sqrt(X**2 + Y**2)) * np.exp(-0.1 * (X**2 + Y**2)) * np.cos(2 * np.pi * X)

    # Initialize the 3D figure
    fig = plt.figure(figsize=(12, 8))
    ax = fig.add_subplot(111, projection='3d')

    # Plot the 3D wave surface with transparency and color mapping
    surf = ax.plot_surface(X, Y, Z, cmap='plasma', edgecolor='none', alpha=0.8)

    # Overlay contour projections on different planes
    ax.contour(X, Y, Z, zdir='z', offset=np.min(Z) - 0.2, cmap='coolwarm', alpha=0.7)
    ax.contour(X, Y, Z, zdir='x', offset=-5.5, cmap='coolwarm', alpha=0.7)
    ax.contour(X, Y, Z, zdir='y', offset=5.5, cmap='coolwarm', alpha=0.7)

    # Customize plot aesthetics
    ax.set_xlabel("Neuronal Activation X", fontsize=12, labelpad=10)
    ax.set_ylabel("Neuronal Activation Y", fontsize=12, labelpad=10)
    ax.set_zlabel("Quantum Wave Function Amplitude", fontsize=12, labelpad=10)
    ax.set_title("3D Neural Quantum Entanglement Waveform", fontsize=14, fontweight='bold')

    # Set view angle for better perspective
    ax.view_init(elev=30, azim=135)

    # Add color bar for better amplitude interpretation
    fig.colorbar(surf, shrink=0.6, aspect=10, label="Amplitude")

    # Show the plot
    plt.show()

# Execute the function to visualize the neural quantum waveform
visualize_3D_neural_waveform()
🔹 Key Features in This Script:
✔ Quantum-Inspired Wave Equation:
Sine and Cosine Functions simulate wave interference.
Exponential Decay mimics neural attenuation over distance.
✔ 3D Surface Plot with Color Mapping:
Uses "plasma" colormap for high-contrast neural activation zones.
Transparency (alpha=0.8) allows better visual depth perception.
✔ Contour Projections on 3D Planes:
Overlays heatmap projections on X, Y, and Z planes.
Helps visualize phase evolution and entanglement-like patterns.
✔ Custom Plot Enhancements:
Labeled axes for better understanding.
View angles optimized for clarity.
Color bar for amplitude interpretation.

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