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 8ฯ
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.





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