Octagonal grid pattern plot Using Python

 import matplotlib.pyplot as plt

import numpy as np

def draw_octagon(ax, center, size):

    """Draws an octagon given a center and size."""

    angles = np.linspace(0, 2 * np.pi, 9)[:-1] + np.pi / 8

    x = center[0] + size * np.cos(angles)

    y = center[1] + size * np.sin(angles)

    ax.plot(np.append(x, x[0]), np.append(y, y[0]), 'b')

def draw_octagonal_grid(rows, cols, size=1.0):

    """Generates a grid of octagons."""

    fig, ax = plt.subplots(figsize=(8, 8))

    dx = 2 * size * np.cos(np.pi / 8)

    dy = 2 * size * np.sin(np.pi / 8) + size

    

    for row in range(rows):

        for col in range(cols):

            x_offset = col * dx

            y_offset = row * dy - (col % 2) * (dy / 2)

            draw_octagon(ax, (x_offset, y_offset), size)

    

    ax.set_aspect('equal')

    ax.axis('off')

    plt.title('octagonal pattern plot')

    plt.show()

rows, cols = 5, 5  

draw_octagonal_grid(rows, cols)

#source code --> clcoding.com 

Code Explanation:

1. Import Required Libraries

import matplotlib.pyplot as plt

import numpy as np

matplotlib.pyplot → Used for plotting the octagons.

numpy → Used for numerical calculations (especially trigonometric functions for octagon vertices).

2. Function to Draw a Single Octagon

def draw_octagon(ax, center, size):

    """Draws an octagon given a center and size."""

This function draws a single octagon at the specified center with a given size.

    angles = np.linspace(0, 2 * np.pi, 9)[:-1] + np.pi / 8

np.linspace(0, 2 * np.pi, 9) → Generates 9 angles from 0 to 

2π (full circle).

[:-1] → Removes the last element, keeping 8 points (for an octagon).

+ np.pi / 8 → Rotates the octagon slightly for proper orientation.

    x = center[0] + size * np.cos(angles)

    y = center[1] + size * np.sin(angles)

Computes the x and y coordinates of the octagon vertices using trigonometric functions:

np.cos(angles) → Calculates x-coordinates.

np.sin(angles) → Calculates y-coordinates.

    ax.plot(np.append(x, x[0]), np.append(y, y[0]), 'b')

np.append(x, x[0]) → Connects the first and last points to close the octagon.

ax.plot(..., 'b') → Plots the octagon outline using a blue ('b') color.

3. Function to Draw an Octagonal Grid

def draw_octagonal_grid(rows, cols, size=1.0):

    """Generates a grid of octagons."""

Defines a function to generate a grid of octagons with given rows, columns, and octagon size.

    fig, ax = plt.subplots(figsize=(8, 8))

Creates a figure (fig) and axes (ax) with a size of 8×8 inches.

    dx = 2 * size * np.cos(np.pi / 8)

    dy = 2 * size * np.sin(np.pi / 8) + size

dx (horizontal spacing) → Uses cosine to calculate the horizontal distance between octagons.

dy (vertical spacing) → Uses sine and size to set the vertical gap between rows.

    for row in range(rows):

        for col in range(cols):

Loops through the grid with rows × cols iterations to draw multiple octagons.

            x_offset = col * dx

            y_offset = row * dy - (col % 2) * (dy / 2)

x_offset = col * dx → Determines the x-coordinate for each octagon.

y_offset = row * dy - (col % 2) * (dy / 2) →

Adjusts vertical alignment so alternate columns are slightly shifted downwards, creating a staggered pattern.

            draw_octagon(ax, (x_offset, y_offset), size)

Calls draw_octagon() to draw an octagon at each calculated position.

    ax.set_aspect('equal')

Ensures equal scaling so the octagons do not appear distorted.

    ax.axis('off')

Hides the x and y axes for a clean visual representation.

    plt.title('octagonal pattern plot')

Sets the plot title.

    plt.show()

Displays the final grid of octagons.

4. Function Call

rows, cols = 5, 5  

draw_octagonal_grid(rows, cols)