𑁍 Torus - Quantum Magnetic Field

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Screen.Recording.2024-07-16.at.23.23.48.mp4

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Introduction

Welcome to the exploration of the Torus and its applications in quantum magnetic fields. This repository is dedicated to understanding the intricate relationship between the toroidal shape and magnetic fields in various contexts, from the microcosmic scale of quantum physics to the macrocosmic scale of astrophysics.

Important Note

We encourage collaboration and discussion on these fascinating topics. If you have any questions or contributions, please feel free to open an issue or submit a pull request.

Torus Mathematically Speaking:

The torus is a doughnut-shaped surface in three-dimensional space, described by the following parametric equations:

$$\color{DodgerBlue} \large \begin{align*} x(\theta, \phi) &= (R + r \cos \theta) \cos \phi \\ y(\theta, \phi) &= (R + r \cos \theta) \sin \phi \\ z(\theta, \phi) &= r \sin \theta \end{align*}$$

where:

• $( \theta )$ and ( \phi ) are angles that trace the surface of the torus,
• $( R )$ is the distance from the center of the torus' tube to the center of the torus,
• ( r ) is the radius of the tube itself.

Quantum Magnetic Field

The torus is a fundamental shape in the study of quantum magnetic fields. This section delves into the creation and dissolution of a torus energy field, exploring how the toroidal geometry plays a crucial role in magnetic confinement and quantum field theory.

Additional Topics

• Da Vinci's Divine Proportion: Investigate the torus in the context of Leonardo da Vinci's studies on divine proportions and its implications in art and science.

✠ ─── ⋆⋅ 𝛂 ♂️ ⋅⋆ ── 𓋹 ─── ⋆⋅♀️ Ω ⋅⋆ ── ✠

*Lσ Rιɳɠɾαȥιαɱσ Dα Vιɳƈι !*

• Human Body Magnetic Quantum Field: Explore the concept of the human body's magnetic field and its potential toroidal structure.

• Earth Magnetic Field: Examine the Earth's magnetic field, which can also be modeled as a torus, and its significance in protecting our planet from solar winds.

Multimedia Content

Included in this repository is the following video file Creation.and.dissolution.of.a.torus.energy.field.mp4 that provides a visual representation of the concepts discussed.

Creation.and.dissolution.of.a.torus.energy.field.mp4

Torus Code

This repository also includes code that demonstrates the generation of a Torus in a programming environment. The code is a practical representation of the parametric equations of the Torus and allows users to visualize and interact with the toroidal shape.

Python Code Example to Generate a Torus

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

# Define the parameters for the torus
R = 1  # Major radius
r = 0.4  # Minor radius

# Create a mesh grid for the angles
theta = np.linspace(0, 2 * np.pi, 100)
phi = np.linspace(0, 2 * np.pi, 100)
theta, phi = np.meshgrid(theta, phi)

# Parametric equations for the torus
X = (R + r * np.cos(theta)) * np.cos(phi)
Y = (R + r * np.cos(theta)) * np.sin(phi)
Z = r * np.sin(theta)

# Create the figure and 3D axis
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')

# Plot the surface with color mapping
ax.plot_surface(X, Y, Z, rstride=5, cstride=5, cmap='coolwarm', edgecolor='none')

# Set the limits of the plot
ax.set_xlim([-2, 2])
ax.set_ylim([-2, 2])
ax.set_zlim([-2, 2])

# Set the viewpoint
ax.view_init(elev=20, azim=30)

# Show the plot
plt.show()

Code Explanation

The code provided is a Python script that generates a three-dimensional plot of a torus using the matplotlib library.

Step-by-Step explanation of what each part of the code does:

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

These lines import the necessary libraries:

• numpy for numerical operations,

• matplotlib.pyplot for plotting graphs,

• mpl_toolkits.mplot3d for 3D plotting capabilities.

  
  

R = 1  # Major radius
r = 0.4  # Minor radius

Here, R and r are defined as the major and minor radii of the torus, respectively.

# Defining the parametric equations of the Torus
theta = np.linspace(0, 2 * np.pi, 100)
phi = np.linspace(0, 2 * np.pi, 100)
theta, phi = np.meshgrid(theta, phi)

These lines create two arrays theta and phi with values ranging from 0 to (2\pi), which represent the angular parameters of the torus. np.meshgrid is then used to create a 2D grid of these angles.

X = (R + r * np.cos(theta)) * np.cos(phi)
Y = (R + r * np.cos(theta)) * np.sin(phi)
Z = r * np.sin(theta)

The parametric equations for the torus are defined here, calculating the (X), (Y), and (Z) coordinates for each point on the torus surface.

# Create the figure and 3D axis
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')

A new figure is created, and a 3D subplot is added to this figure.

# Plot the surface with color mapping
ax.plot_surface(X, Y, Z, rstride=5, cstride=5, cmap='coolwarm', edgecolor='none')

This line plots the surface of the torus. rstride and cstride control the row and column stride, cmap sets the color map, and edgecolor is set to ‘none’ to not draw borders around the surface patches.

# Set the limits of the plot
ax.set_xlim([-2, 2])
ax.set_ylim([-2, 2])
ax.set_zlim([-2, 2])

The limits of the (x), (y), and (z) axes are set to range from -2 to 2.

# Set the viewpoint
ax.view_init(elev=20, azim=30)

The viewpoint of the plot is set with an elevation of 20 degrees and an azimuth of 30 degrees.

plt.show()

Finally, this line displays the following plot.

Each part of the code contributes to creating a visual representation of a torus in 3D space, with specific coloring and viewpoint settings

This script is a practical application of mathematical concepts in computer graphics and can be used for educational purposes or in simulations that require a visual representation of a torus.

If you have any questions or need further clarification, feel free to open a pull request and ask.

Copyright 2024 Quantum Software Development. Code released under the MIT license.