Sunflower Spiral pattern using python

 

import numpy as np

import matplotlib.pyplot as plt

n=1000

golden_angle=np.pi*(3-np.sqrt(5))

theta=np.arange(n)*golden_angle

r=np.sqrt(np.arange(n))

x=r*np.cos(theta)

y=r*np.sin(theta)

plt.figure(figsize=(6,6))

plt.scatter(x,y,s=5,c=np.arange(n),cmap="viridis",alpha=0.75)

plt.axis('off')

plt.title('Sunflower spiral pattern')

plt.show()

#source code --> clcoding.com 

Code Explanation:

1. Importing Required Libraries

import numpy as np

import matplotlib.pyplot as plt

numpy: Used for numerical operations (angles, radius, and Cartesian coordinates).

matplotlib.pyplot: Used to create and display the plot.

 2. Define Number of Points (Seeds)

n = 1000

n is the total number of seeds in the pattern.

Higher values of n produce denser spirals.

 3. Calculate the Golden Angle

golden_angle = np.pi * (3 - np.sqrt(5))

The golden angle (~137.5° in radians) is derived from the golden ratio (Φ ≈ 1.618).

This angle ensures optimal packing, just like real sunflower seeds.

 4. Generate Angular and Radial Coordinates

theta = np.arange(n) * golden_angle 

r = np.sqrt(np.arange(n))

theta = np.arange(n) * golden_angle:

Each seed is rotated by golden_angle to create a spiral effect.

r = np.sqrt(np.arange(n)):

Controls the radial distance of seeds.

The square root ensures even spacing outward.

 5. Convert to Cartesian Coordinates

x = r * np.cos(theta)

y = r * np.sin(theta)

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

cos() and sin() help place the seeds in a circular pattern.

 6. Plot the Spiral

plt.figure(figsize=(6, 6))  # Define figure size

plt.scatter(x, y, s=5, c=np.arange(n), cmap="viridis", alpha=0.75) 

plt.scatter(x, y, s=5, c=np.arange(n), cmap="viridis", alpha=0.75)

x, y: Seed positions.

s=5: Size of each seed.

c=np.arange(n): Color gradient based on seed index.

cmap="viridis": Uses a color gradient.

alpha=0.75: Sets transparency.

 7. Remove Axes and Add Title

plt.axis("off")  # Hides axes

plt.title('Sunflower Spiral Pattern')  # Adds a title

plt.axis("off"): Removes unnecessary axes.

plt.title('Sunflower Spiral Pattern'): Labels the figure.

 8. Display the Plot

plt.show()

Renders the final visualization.