Gravitational Wave Simulation Pattern using Python

 

import numpy as np

import matplotlib.pyplot as plt

from mpl_toolkits.mplot3d import Axes3D

x = np.linspace(-5, 5, 100)

y = np.linspace(-5, 5, 100)

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

frequency=3

wavelength=2

amplitude=1

time=0

Z = amplitude * np.sin(frequency * (X**2 + Y**2)**0.5 - time) * np.exp(-0.2 * (X**2 + Y**2))

fig=plt.figure(figsize=(10,7))

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

ax.plot_surface(X,Y,Z,cmap="coolwarm",edgecolor="none")

ax.set_xlabel("X Axis")

ax.set_ylabel("Y Axis")

ax.set_zlabel("Space Time Curvature")

ax.set_title("Gravitation tides Wave simulation")

ax.set_xticks([])

ax.set_yticks([])

ax.set_zticks([])

plt.show()

#source code --> clcoding.com 

Code Explanation:

1. Import Required Libraries

 import numpy as np

import matplotlib.pyplot as plt

from mpl_toolkits.mplot3d import Axes3D

NumPy (np): Used for numerical computations and generating grid points.

 Matplotlib (plt): Used for plotting the 3D gravitational wave surface.

 mpl_toolkits.mplot3d: Enables 3D plotting.

 

2. 2Define the Grid for the Simulation

 x = np.linspace(-5, 5, 100)  # X-axis range (-5 to 5) with 100 points

y = np.linspace(-5, 5, 100)  # Y-axis range (-5 to 5) with 100 points

X, Y = np.meshgrid(x, y)     # Create a 2D mesh grid from x and y values

np.linspace(-5, 5, 100): Creates 100 evenly spaced points in the range [-5, 5] for x and y axes.

 np.meshgrid(x, y): Generates a grid of (X, Y) coordinates, forming a 2D plane where the wave will be calculated.

 

3.Define Gravitational Wave Parameters

 frequency = 3  # Number of oscillations per unit distance

wavelength = 2  # Distance between peaks (not directly used here)

amplitude = 1  # Maximum wave height

time = 0  # Static snapshot (can animate later)

frequency: Controls how many oscillations (wave peaks) occur in the simulation.

 wavelength: Represents the distance between peaks (not directly used in this equation).

 amplitude: Defines the height of the wave (maximum space-time distortion).

 time = 0: For a static snapshot; can be animated to show real-time wave evolution.

 

4. Compute the 3D Gravitational Wave Surface

Z = amplitude * np.sin(frequency * (X**2 + Y**2)**0.5 - time) * np.exp(-0.2 * (X**2 + Y**2))

This equation models the gravitational wave pattern:

Wave Component (sin(f * r - t)):

 r = (X² + Y²)^(0.5): Represents the radial distance from the center (like ripples on water).

 sin(frequency * r - time): Creates oscillations (wave-like structure).

 Damping Component (exp(-0.2 * r^2)):

 The exponential decay ensures that waves fade as they move outward.

 Models how gravitational waves weaken over long distances (like real astrophysical waves).

 Multiplication with amplitude: Scales the wave intensity.

 

5.Create the 3D Figure and Axes

fig = plt.figure(figsize=(10, 7))

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

figsize=(10,7): Sets the figure size for a better view.

 ax = fig.add_subplot(111, projection="3d"): Creates a 3D plot using Matplotlib.

 

6.Plot the Gravitational Wave Surface

 ax.plot_surface(X, Y, Z, cmap="coolwarm", edgecolor="none")

plot_surface(X, Y, Z): Creates a 3D surface plot from the computed values.

 cmap="coolwarm": Uses a blue-red colormap to highlight the wave crests and troughs.

 edgecolor="none": Removes edge lines for a smooth visualization.

 

7. Add Labels and Title

ax.set_xlabel("X Axis")

ax.set_ylabel("Y Axis")

ax.set_zlabel("Space-Time Curvature")

ax.set_title(" Gravitational Tides – 3D Gravitational Wave Simulation")

Labels each axis to indicate spatial directions and wave intensity.

 Title describes the astrophysical concept being visualized.

 

8.Remove Grid Ticks for a Clean Look

ax.set_xticks([])

ax.set_yticks([])

ax.set_zticks([])

Removes axis ticks to make the plot clean and visually appealing.

 
9. Display the Final 3D Plot

 plt.show()

Displays the gravitational wave simulation.