Chrono Web Pattern using Python

 

import numpy as np

import matplotlib.pyplot as plt

from mpl_toolkits.mplot3d import Axes3D

r = np.linspace(0.1, 5, 200)

theta = np.linspace(0, 2 * np.pi, 200)

r, theta = np.meshgrid(r, theta)

X = r * np.cos(theta)

Y = r * np.sin(theta)

Z = np.sin(4 * theta - 2 * r) * np.exp(-0.1 * r)

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

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

ax.plot_surface(X, Y, Z, cmap='viridis', edgecolor='black', linewidth=0.1)

ax.set_title('Chrono Web', fontsize=18, fontweight='bold')

ax.axis('off')

ax.view_init(elev=30, azim=45)

plt.tight_layout()

plt.show()

#source code --> clcoding.com

Code Explanation:

1. Importing Libraries

import numpy as np

import matplotlib.pyplot as plt

from mpl_toolkits.mplot3d import Axes3D

numpy is used for numerical operations, especially for creating arrays and mathematical functions.

matplotlib.pyplot is the plotting library used for visualization.

mpl_toolkits.mplot3d enables 3D plotting capabilities in matplotlib.

2. Create the Polar Grid

r = np.linspace(0.1, 5, 200)

theta = np.linspace(0, 2 * np.pi, 200)

r, theta = np.meshgrid(r, theta)

r (radius) goes from 0.1 to 5 in 200 steps.

theta (angle) goes from 0 to 2π (a full circle) in 200 steps.

np.meshgrid creates a 2D grid from these vectors, so we can calculate X, Y, and Z values over the full polar coordinate system.

3. Convert Polar Coordinates to Cartesian

X = r * np.cos(theta)

Y = r * np.sin(theta)

Converts each point in the polar grid into Cartesian coordinates.

This is needed because matplotlib 3D plots are in X-Y-Z space.

4. Define Z Values (Height) – the "Chrono Web" Pattern

Z = np.sin(4 * theta - 2 * r) * np.exp(-0.1 * r)

This formula creates radial sine wave ripples.

4 * theta gives a rotational (angular) ripple with 4 waves per rotation.

-2 * r makes the wave shift inward or outward, creating a spiraling effect.

np.exp(-0.1 * r) damps the wave amplitude as the radius increases — simulating fading over distance, like time decay.

5. Set Up the Plot

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

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

fig = plt.figure(...) creates the figure window with a specific size.

add_subplot(..., projection='3d') initializes a 3D plot.

6. Draw the Surface

ax.plot_surface(X, Y, Z, cmap='viridis', edgecolor='black', linewidth=0.1)

plot_surface draws a 3D surface.

cmap='viridis' gives a smooth color gradient.

edgecolor='black', linewidth=0.1 adds a subtle grid to give a web-like structure.

7. Customize the Plot

ax.set_title('Chrono Web', fontsize=18, fontweight='bold')

ax.axis('off')

ax.view_init(elev=30, azim=45)

set_title(...) adds a bold title to the plot.

axis('off') hides the axes for a cleaner, more artistic look.

view_init(...) sets the camera angle (elevation = 30°, azimuth = 45°) for 3D viewing.

8. Final Layout and Display

plt.tight_layout()

plt.show()

tight_layout() adjusts the spacing to fit all elements nicely.

plt.show() renders the plot window and displays the final "Chrono Web" 3D pattern.