3D Butterfly Wing (Mathematical Model) using Python

 

import matplotlib.pyplot as plt

import numpy as np

u=np.linspace(0,2*np.pi,100)

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

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

x=np.sin(u)*(1+0.5*np.cos(v))*np.cos(v)

y=np.cos(u)*(1+0.5*np.cos(v))*np.cos(v)

z=np.sin(v)+0.2*np.sin(3*u)

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

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

ax.plot_surface(x,y,z,cmap='coolwarm',edgecolor='k',alpha=0.9)

ax.set_title('3D Butterfly Wing')

ax.set_xlabel('X axis')

ax.set_ylabel('Y axis')

ax.set_zlabel('Z axis')

ax.set_box_aspect([1,1,0.5])

plt.tight_layout()

plt.show()

#source code --> clcoding.com 

Code Explanation:

1. Importing Libraries

import numpy as np

import matplotlib.pyplot as plt

numpy: Used for creating numerical arrays and trigonometric functions.

 matplotlib.pyplot: Used for creating the 3D plot.

 2. Creating Parameter Grids

u = np.linspace(0, 2 * np.pi, 100)

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

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

u: Controls the angular direction (think of it like horizontal spread of the wing).

 v: Controls the vertical sweep or curvature of the wings.

 meshgrid: Creates a 2D grid to evaluate the parametric surface over.

 3. Defining the Parametric Equations

x = np.sin(u) * (1 + 0.5 * np.cos(v)) * np.cos(v)

y = np.cos(u) * (1 + 0.5 * np.cos(v)) * np.cos(v)

z = np.sin(v) + 0.2 * np.sin(3 * u)

These equations build a curved, sinusoidal surface that resembles butterfly wings:

 x and y: Give a spiraling shape using a modified polar coordinate system.

 The term (1 + 0.5 * cos(v)) * cos(v) gives depth and curvature.

 z: Controls the vertical deformation, making the wings appear "flapping" or "wavy."

 sin(v) gives the main vertical structure.

 0.2 * sin(3 * u) adds a ripple or flutter pattern, mimicking wing detail.

 4. Setting Up the 3D Plot

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

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

Creates a square figure with a 3D plotting environment.

 5. Plotting the Surface

ax.plot_surface(x, y, z, cmap='coolwarm', edgecolor='k', alpha=0.9)

plot_surface: Draws the 3D shape.

 cmap='coolwarm': Uses a smooth gradient of blue to red.

 edgecolor='k': Adds a black gridline for better surface structure visibility.

 alpha=0.9: Slight transparency for softness.

 6. Customizing the Axes

ax.set_title('3D Butterfly Wings (Mathematical Model)', fontsize=14)

ax.set_xlabel('X axis')

ax.set_ylabel('Y axis')

ax.set_zlabel('Z axis')

ax.set_box_aspect([1, 1, 0.5])

Adds title and axis labels.

 set_box_aspect([1, 1, 0.5]): Makes the Z-axis compressed to enhance the wing appearance.

7. Show the Plot

plt.tight_layout()

plt.show()

tight_layout(): Adjusts padding between plot elements.

 show(): Displays the 3D plot.