3D Conch Shell Structure using Python

 

import numpy as np

import matplotlib.pyplot as plt

from mpl_toolkits.mplot3d import Axes3D

theta = np.linspace(0, 8 * np.pi, 500)   

z = np.linspace(0, 2, 500)               

r = z**2 + 0.1                           

phi = np.linspace(0, 2 * np.pi, 50)

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

z = np.linspace(0, 2, 500)

z = np.tile(z, (50, 1))

r = z**2 + 0.1

x = r * np.cos(theta) * np.cos(phi)

y = r * np.sin(theta) * np.cos(phi)

z = r * np.sin(phi)

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

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

ax.plot_surface(x, y, z, cmap='copper', edgecolor='none', alpha=0.9)

ax.set_title('3D Conch Shell ', fontsize=14)

ax.set_box_aspect([1,1,1])

ax.axis('off') 

plt.show()

#source code --> clcoding.com

Code Explanation:

1. Import Libraries

import numpy as np

import matplotlib.pyplot as plt

from mpl_toolkits.mplot3d import Axes3D

numpy is for numerical arrays and functions.

matplotlib is for plotting.

Axes3D is needed to enable 3D plotting in matplotlib. 

2. Define Spiral Parameters

theta_vals = np.linspace(0, 8 * np.pi, 500)  # Spiral angle: 0 to 8π

z_vals = np.linspace(0, 2, 500)              # Vertical height

phi_vals = np.linspace(0, 2 * np.pi, 50)     # Circular angle around shell's axis

theta_vals: Controls how many times the spiral wraps around — 4 full rotations.

z_vals: The height (like vertical position in the shell).

phi_vals: Describes the circle at each spiral point (the shell's cross-section). 

3. Create 2D Grids

theta, phi = np.meshgrid(theta_vals, phi_vals)

meshgrid creates a 2D grid so we can compute (x, y, z) coordinates across both theta and phi.

theta and phi will be shape (50, 500) so that we can build a surface. 

4. Define Radius and Z

z = np.linspace(0, 2, 500)

z = np.tile(z, (50, 1))       # Repeat z rows to shape (50, 500)

r = z**2 + 0.1                # Radius grows quadratically with height

z is tiled to match the (50, 500) shape of theta and phi.

r = z^2 + 0.1: Makes the radius increase faster as you go up, giving the shell its expanding spiral. 

5. Compute 3D Coordinates

x = r * np.cos(theta) * np.cos(phi)

y = r * np.sin(theta) * np.cos(phi)

z = r * np.sin(phi)

This is the parametric equation for a growing spiral swept by a circle.

theta sweeps the spiral.

phi creates a circular cross-section at each spiral point. 

The cos(phi) and sin(phi) give the circular shape.

r * cos(theta) and r * sin(theta) give the spiral path. 

6. Plotting the Shell

 fig = plt.figure(figsize=(10, 8))

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

 ax.plot_surface(x, y, z, cmap='copper', edgecolor='none', alpha=0.9)

ax.set_title('3D Conch Shell Structure', fontsize=14)

ax.set_box_aspect([1,1,1])

ax.axis('off')

plt.show()

plot_surface(...): Renders a 3D surface using x, y, z.

 cmap='copper': Gives it a warm, shell-like color.

 ax.axis('off'): Hides the axis to enhance the visual aesthetics.

 set_box_aspect([1,1,1]): Keeps the plot from being stretched.