Galaxy Swirl Pattern using Python

 

import numpy as np

import matplotlib.pyplot as plt

num_stars=1000

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

r=np.exp(0.3*theta)

noise=np.random.normal(scale=0.2,size=(num_stars,2))

x=r*np.cos(theta)+noise[:,0]

y=r*np.sin(theta)+noise[:,-1]

plt.figure(figsize=(6,6),facecolor="black")

plt.scatter(x,y,color="white",s=2)

plt.scatter(-x,-y,color="white",s=2)

plt.axis('off')

plt.title("Galaxy swirl pattern",fontsize=14,color="white")

plt.show()

#source code --> clcoding.com

Code Explanation

Step 1: Import Required Libraries

import numpy as np

import matplotlib.pyplot as plt

numpy (np): Used for numerical computations, like creating arrays, generating random values, and performing trigonometric calculations.

matplotlib.pyplot (plt): Used for creating and customizing the visualization.

Step 2: Define the Number of Stars

num_stars = 1000  

This sets the total number of stars that will be plotted in the galaxy.

A larger number (e.g., 5000) would create a denser galaxy.

Step 3: Generate Spiral Angle (θ)

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

theta represents the angle in radians.

np.linspace(0, 4 * np.pi, num_stars) generates 1000 values from 0 to 4π (two full turns).

This controls the swirl or spiral effect in the galaxy.

Step 4: Compute Spiral Radius (r)

r = np.exp(0.3 * theta)  

This is the equation of a logarithmic spiral:

r=e 0.3θ

 exp(0.3 * theta) ensures that the spiral expands outward as theta increases.

The factor 0.3 controls the tightness of the swirl:

Lower values (e.g., 0.2) → Tighter spiral.

Higher values (e.g., 0.5) → More open swirl.

Step 5: Introduce Random Noise (Star Distribution)

noise = np.random.normal(scale=0.2, size=(num_stars, 2))

This adds randomness to the star positions to make them look more natural.

np.random.normal(scale=0.2, size=(num_stars, 2)):

Generates Gaussian noise with a mean of 0 and a standard deviation of 0.2.

The shape (num_stars, 2) means each star gets a random X and Y offset.

This makes the stars appear slightly scattered instead of forming a perfect spiral.

Step 6: Convert Polar Coordinates to Cartesian Coordinates

x = r * np.cos(theta) + noise[:, 0]

y = r * np.sin(theta) + noise[:, 1]

Converts the polar coordinates (r, theta) into Cartesian coordinates (x, y).

Equations:

x=r⋅cos(θ)+random noise

y=r⋅sin(θ)+random noise

The random noise slightly shifts each star away from the perfect spiral, creating a realistic galaxy.

Step 7: Set Up the Plot with a Black Background

plt.figure(figsize=(8, 8), facecolor="black")

Creates a new figure with a square aspect ratio (8×8 inches).

facecolor="black" sets the background color to black for a space-like appearance.

Step 8: Plot the Stars (White Dots)

plt.scatter(x, y, color="white", s=2)  

plt.scatter(x, y, color="white", s=2):

Plots each star as a tiny white dot.

s=2: Controls the size of each star (can be increased for a brighter look).

Step 9: Create a Symmetric Swirl

plt.scatter(-x, -y, color="white", s=2)

This mirrors the swirl in the opposite direction.

Instead of just x, y, we plot -x, -y to create a symmetric pattern, making the galaxy more balanced.

Step 10: Hide the Axes for a Clean Look

plt.axis("off")

Removes the X and Y axes, making the visualization look more like deep space.

Step 11: Add a Title

plt.title("Galaxy Swirl Pattern", fontsize=14, color="white")

Adds a title "Galaxy Swirl Pattern" in white color.

Step 12: Display the Final Plot

plt.show()

Renders the final galaxy swirl on the screen.