Enneper Surface Pattern using Python

 

import matplotlib.pyplot as plt

import numpy as np

from mpl_toolkits.mplot3d import Axes3D

u=np.linspace(-2,2,100)

v=np.linspace(-2,2,100)

U,V=np.meshgrid(u,v)

X=U-(U**3)/3+U*V**2

Y=V-(V**3)/3+V*U**2

Z=U**2-V**2

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

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

ax.plot_surface(X,Y,Z,cmap='viridis',edgecolor='none',alpha=0.9)

ax.set_title('Enneper Surface')

ax.set_xlabel('X')

ax.set_ylabel('Y')

ax.set_zlabel('Z')

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: For numerical operations and creating arrays.

Matplotlib.pyplot: For plotting graphs.

Axes3D: Enables 3D plotting capabilities.

 2. Define Parameter Grid

u = np.linspace(-2, 2, 100)

v = np.linspace(-2, 2, 100)

U, V = np.meshgrid(u, v)

Creates two arrays u and v with 100 points each from -2 to 2.

np.meshgrid creates coordinate matrices U and V for all combinations of u and v. This forms a grid over which the surface is calculated.

 3. Calculate Coordinates Using Parametric Equations

X = U - (U**3)/3 + U*V**2

Y = V - (V**3)/3 + V*U**2

Z = U**2 - V**2

Computes the 3D coordinates of the Enneper surface using its parametric formulas:

 4. Create Figure and 3D Axis

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

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

Creates a new figure with size 10x8 inches.

 Adds a 3D subplot to the figure for 3D plotting.

 5. Plot the Surface

ax.plot_surface(X, Y, Z, cmap='viridis', edgecolor='none', alpha=0.9)

Plots a 3D surface using the (X, Y, Z) coordinates.

 Uses the 'viridis' colormap for coloring the surface.

 Removes edge lines for a smooth look.

 Sets surface transparency to 90% opacity for better visual depth.

 6. Set Titles and Axis Labels

ax.set_title('Enneper Surface')

ax.set_xlabel('X')

ax.set_ylabel('Y')

ax.set_zlabel('Z')

Adds a title and labels to the X, Y, and Z axes.

 7. Display the Plot

plt.show()

Shows the final 3D plot window displaying the Enneper surface.