Arc Twirl Pattern using Python

 

import numpy as np

import matplotlib.pyplot as plt

theta = np.linspace(0, 6 * np.pi, 1000)

r = 1 + 0.2 * np.sin(5 * theta)

x = r * np.cos(theta)

y = r * np.sin(theta)

plt.figure(figsize=(7, 7))

plt.plot(x, y, color='teal', linewidth=2)

for i in range(1, 6):

    arc_theta = np.linspace(0, 2 * np.pi / i, 300)

    arc_r = 0.8 + 0.1 * i

    arc_x = arc_r * np.cos(arc_theta)

    arc_y = arc_r * np.sin(arc_theta)

    plt.plot(arc_x, arc_y, color='darkcyan', linewidth=1.5, alpha=0.6)

plt.gca().set_aspect('equal')

plt.axis('off')

plt.title('Arc Twirl Pattern')

plt.show()

#source code --> clcoding.com 

Code Explanation:

1. Import Libraries

import numpy as np

import matplotlib.pyplot as plt

numpy: Used for numerical operations like generating a range of values for the angles and radii.

matplotlib.pyplot: Used for plotting and visualizing the pattern.

2. Define Parameters for the Arc Twirl Effect

theta = np.linspace(0, 6 * np.pi, 1000)

r = 1 + 0.2 * np.sin(5 * theta)

theta: Creates a range of 1000 values between 0 and 6 * np.pi (approximately 18.85). This is the angle parameter used to generate the spiral.

r: The radius at each angle theta is calculated. The formula 1 + 0.2 * np.sin(5 * theta) introduces oscillations to the radius as theta increases, which creates a twirling effect.

3. Convert Polar Coordinates to Cartesian Coordinates

x = r * np.cos(theta)

y = r * np.sin(theta)

x and y: Convert the polar coordinates (r, theta) into Cartesian coordinates (x, y) using the formulas:

x = r * cos(theta)

y = r * sin(theta)

These are the coordinates needed to plot the spiral pattern on a 2D graph.

4. Create the Plot

plt.figure(figsize=(7, 7))

plt.plot(x, y, color='teal', linewidth=2)

plt.figure(figsize=(7, 7)): Creates a new figure with a square aspect ratio of 7x7 inches.

plt.plot(x, y, color='teal', linewidth=2): Plots the spiral defined by the x and y values with a teal color and a line width of 2. This creates the main spiral pattern.

5. Adding Arcs with Variation

for i in range(1, 6):

    arc_theta = np.linspace(0, 2 * np.pi / i, 300)

    arc_r = 0.8 + 0.1 * i

    arc_x = arc_r * np.cos(arc_theta)

    arc_y = arc_r * np.sin(arc_theta)

    plt.plot(arc_x, arc_y, color='darkcyan', linewidth=1.5, alpha=0.6)

for i in range(1, 6): A loop that generates 5 additional arc patterns, each with a different radius and number of points.

arc_theta: For each arc, arc_theta is a range of angles from 0 to 2 * np.pi / i with 300 points, which defines how much of a full circle the arc will cover.

arc_r: The radius for each arc starts at 0.8 and increases by 0.1 * i in each iteration. This creates expanding arcs with each loop iteration.

arc_x and arc_y: These calculate the x and y Cartesian coordinates for the arcs.

plt.plot(arc_x, arc_y, color='darkcyan', linewidth=1.5, alpha=0.6): Plots the arcs using a darkcyan color, with a line width of 1.5 and transparency (alpha=0.6) to give them a subtle appearance, allowing the main spiral to remain prominent.

6. Styling

plt.gca().set_aspect('equal')

plt.axis('off')

plt.title("Arc Twirl", fontsize=20, color='teal')

plt.gca().set_aspect('equal'): Sets the aspect ratio to "equal," meaning the units on the x and y axes are scaled equally. This ensures that the arcs and spiral remain circular rather than stretched.

plt.axis('off'): Turns off the axis lines and labels for a clean look.

plt.title("Arc Twirl", fontsize=20, color='teal'): Adds a title to the plot "Arc Twirl" in a teal color with a font size of 20.

7. Display the Plot

plt.show()

plt.show(): Displays the final plot with all the arcs and spiral patterns.