Velvet Nebula Pattern using Python

import numpy as np

import matplotlib.pyplot as plt

from mpl_toolkits.mplot3d import Axes3D

theta=np.linspace(0,4*np.pi,400)

z=np.linspace(-2,2,400)

r=z**2+1

x=r*np.sin(theta)

y=r*np.cos(theta)

fig=plt.figure(figsize=(10,8))

ax=fig.add_subplot(111,projection='3d')

colors=np.linspace(0,1,len(x))

ax.scatter(x,y,z,c=colors,cmap='plasma',s=10)

ax.set_xlabel('X Axis')

ax.set_ylabel('Y Axis')

ax.set_zlabel('Z Axis')

ax.set_title('Velvet Nebula Bloom')

plt.show()

#source code --> clcoding.com

 Code Explanation:

import numpy as np

import matplotlib.pyplot as plt

from mpl_toolkits.mplot3d import Axes3D

 

import numpy as np:

Imports the NumPy library using the alias np.

NumPy is used for efficient numerical calculations and generating arrays of data points.

 

import matplotlib.pyplot as plt:

Imports Matplotlib’s pyplot module using the alias plt.

It provides functions to plot graphs, charts, and visualizations.

 

from mpl_toolkits.mplot3d import Axes3D:

Imports Axes3D from the mpl_toolkits.mplot3d module.

It allows creating 3D plots using Matplotlib.

 

2. Generate Data for the Spiral

a) Theta - Angle Generation

theta = np.linspace(0, 4 * np.pi, 400)

np.linspace(start, stop, num):

Generates 400 evenly spaced values from 0 to 4π (approx 12.566).

theta represents the angle in radians for a circular or spiral motion.

This variable will be used to define the x and y coordinates using sine and cosine functions.

 

b) Z - Vertical Axis (Height)

z = np.linspace(-2, 2, 400)

Generates 400 points from -2 to 2, representing the Z-axis (height).

This makes the spiral extend vertically from -2 to 2 units.

 

c) R - Spiral Radius

r = z**2 + 1

This creates a varying radius using the formula:

𝑟=𝑧2+1

 

Explanation:

At the center (z = 0), the radius is 1.

As z increases or decreases, the radius expands because  increases.

This makes the spiral bloom outward, resembling a nebula.

 

d) Calculate X and Y Coordinates

x = r * np.sin(theta)

y = r * np.cos(theta)

x = r × sin(θ) and y = r × cos(θ):

 

These parametric equations define the position of points in a circular (spiral) pattern.

sin() and cos() determine the coordinates on the XY-plane.

r controls how far the points are from the origin, forming a widening spiral.

 

3. Create the Plot

fig = plt.figure(figsize=(12, 8))

ax = fig.add_subplot(111, projection='3d')

plt.figure(figsize=(12, 8)):

Creates a figure with a size of 12x8 inches for better visualization.

fig.add_subplot(111, projection='3d'):

Adds a 3D subplot to the figure.

111 means 1 row, 1 column, and this is the first subplot.

projection='3d' enables 3D plotting.

 

4. Apply a Color Gradient

colors = np.linspace(0, 1, len(x))

np.linspace(0, 1, len(x)):

Generates an array of values from 0 to 1 to map colors.

len(x) ensures there is one color for each point.

These values will be used to create a smooth gradient using a colormap.

 

Plot the Spiral Using Scatter Plot

ax.scatter(x, y, z, c=colors, cmap='plasma', s=10)

ax.scatter():

 

Creates a 3D scatter plot.

Each point is represented as a small dot in 3D space.

Parameters:

x, y, z: Coordinates for each point.

c=colors: The color values for each point (gradient).

cmap='plasma': Uses the Plasma colormap, giving a vibrant velvet glow.

s=10: Sets the size of the points to 10 pixels.

 

5. Add Axis Labels and Title

ax.set_xlabel('X Axis')

ax.set_ylabel('Y Axis')

ax.set_zlabel('Z Axis')

ax.set_title('Velvet Nebula Bloom: 3D Spiral Pattern using Matplotlib')

ax.set_xlabel(): Labels the X-axis.

ax.set_ylabel(): Labels the Y-axis.

ax.set_zlabel(): Labels the Z-axis.

ax.set_title(): Sets the plot title, describing the visualization as Velvet Nebula Bloom.

 

6. Display the Plot

plt.show()

plt.show():

Renders the plot and displays it in a window.

You can rotate, zoom, and explore the plot using the interactive Matplotlib interface.