Plot a vector field over the axes in Python Matplotlib?

A vector field displays vectors as arrows at different points in a coordinate system. In Python Matplotlib, we use the quiver() function to plot vector fields, where each arrow represents the direction and magnitude of vectors at specific coordinates.

Syntax

plt.quiver(X, Y, U, V, C, **kwargs)

Where:

• X, Y − Grid coordinates for arrow positions

• U, V − Vector components (arrow directions)

• C − Optional array for color mapping

Example

Let's create a circular vector field using polar coordinates ?

import numpy as np
import matplotlib.pyplot as plt

# Set figure size
plt.rcParams["figure.figsize"] = [7.50, 3.50]
plt.rcParams["figure.autolayout"] = True

# Create grid coordinates
n = 8
X, Y = np.mgrid[0:n, 0:n]

# Calculate polar coordinates from center
T = np.arctan2(Y - n / 2., X - n / 2.)
R = 10 + np.sqrt((Y - n / 2.0) ** 2 + (X - n / 2.0) ** 2)

# Calculate vector components
U, V = R * np.cos(T), R * np.sin(T)

# Create the plot
plt.axes([0.025, 0.025, 0.95, 0.95])
plt.quiver(X, Y, U, V, R, cmap="copper")

plt.show()

Output

How It Works

The vector field creation involves these key steps:

• Grid Creation − np.mgrid[0:n, 0:n] creates coordinate matrices

• Polar Conversion − np.arctan2() calculates angles from center

• Vector Components − U, V represent x and y direction components

• Color Mapping − R values determine arrow colors via colormap

Key Parameters

Conclusion

The quiver() function effectively visualizes vector fields by plotting directional arrows. Use polar coordinates for circular patterns and adjust colormap parameters to enhance visual clarity of vector magnitudes and directions.