Sand Dune Ripple Pattern using Python

 

import numpy as np

import matplotlib.pyplot as plt

width, height = 800, 400

frequency = 0.1  

amplitude = 10  

x = np.linspace(0, 10, width)

y = np.linspace(0, 5, height)

X, Y = np.meshgrid(x, y)

Z = amplitude*np.sin(2*np.pi*frequency*X+np.pi/4*np.sin(2*np.pi*frequency* Y))

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

plt.imshow(Z,cmap='copper',extent=(0,10,0,5))

plt.colorbar(label='Height')

plt.title('Sand Dune Ripple Pattern')

plt.xlabel('X')

plt.ylabel('Y')

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

Import essential libraries for numerical operations and 3D plotting.

 

2. Create 2D Grid

x = np.linspace(-10, 10, 200)

y = np.linspace(-10, 10, 200)

X, Y = np.meshgrid(x, y)

Define linearly spaced points for x and y axes.

Create a mesh grid covering the 2D plane where waves will be calculated.

 

3. Define Signal Sources

sources = [

    {'center': (-3, -3), 'freq': 2.5},

    {'center': (3, 3), 'freq': 3.0},

    {'center': (-3, 3), 'freq': 1.8},

]

Define multiple wave sources with positions and frequencies.

 

4. Initialize Amplitude Matrix

Z = np.zeros_like(X)

Initialize a zero matrix to store combined wave amplitudes for each grid point.

 

5. Calculate Wave Contributions from Each Source

for src in sources:

    dx = X - src['center'][0]

    dy = Y - src['center'][1]

    r = np.sqrt(dx**2 + dy**2) + 1e-6

    Z += np.sin(src['freq'] * r) / r

For each source:

Compute distance from every grid point to the source.

Calculate decaying sine wave amplitude.

Add this to the total amplitude matrix.

 

6. Set Up 3D Plot

fig = plt.figure(figsize=(12, 8))

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

Create a figure and add a 3D subplot.

 

7. Plot the Signal Interference Mesh

ax.plot_wireframe(X, Y, Z, rstride=3, cstride=3, color='mediumblue', alpha=0.8, linewidth=0.5)

Plot the wireframe mesh representing the combined wave interference pattern.

 

8. Add Titles and Labels

ax.set_title("Signal Interference Mesh", fontsize=16)

ax.set_xlabel("X")

ax.set_ylabel("Y")

ax.set_zlabel("Amplitude")

Label the plot and axes.

 

9. Adjust Aspect Ratio

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

Adjust the 3D box aspect ratio for better visualization.

 

10. Display the Plot

plt.tight_layout()

plt.show()

Optimize layout and render the final plot on screen.