Quiver Plots

Quiver plots visualize vector fields using arrows to show direction and magnitude.

Basic Quiver Plot

import matplotlib.pyplot as plt
import numpy as np

x = np.arange(0, 5, 1)
y = np.arange(0, 5, 1)
X, Y = np.meshgrid(x, y)

U = np.ones_like(X)  # x-component
V = np.ones_like(Y)  # y-component

fig, ax = plt.subplots()
ax.quiver(X, Y, U, V)
ax.set_title('Basic Quiver Plot')
plt.show()

Vector Field Example

x = np.linspace(-2, 2, 10)
y = np.linspace(-2, 2, 10)
X, Y = np.meshgrid(x, y)

# Circular field: F = (-y, x)
U = -Y
V = X

fig, ax = plt.subplots()
ax.quiver(X, Y, U, V)
ax.set_aspect('equal')
ax.set_title('Circular Vector Field')
plt.show()

Key Parameters

Parameter	Description	Default
X, Y	Arrow positions	Required
U, V	Arrow components	Required
scale	Arrow length scaling	Auto
width	Arrow shaft width	0.005
headwidth	Head width	3
headlength	Head length	5
color	Arrow color	'k'

Color by Magnitude

x = np.linspace(-2, 2, 15)
y = np.linspace(-2, 2, 15)
X, Y = np.meshgrid(x, y)

U = -Y
V = X
magnitude = np.sqrt(U**2 + V**2)

fig, ax = plt.subplots()
q = ax.quiver(X, Y, U, V, magnitude, cmap='viridis')
plt.colorbar(q, label='Magnitude')
ax.set_aspect('equal')
plt.show()

Normalized Arrows (Direction Only)

magnitude = np.sqrt(U**2 + V**2)
U_norm = U / magnitude
V_norm = V / magnitude

fig, ax = plt.subplots()
ax.quiver(X, Y, U_norm, V_norm)
ax.set_aspect('equal')
plt.show()

Add Legend (quiverkey)

fig, ax = plt.subplots()
q = ax.quiver(X, Y, U, V)
ax.quiverkey(q, X=0.85, Y=1.05, U=2, label='2 units', labelpos='E')
plt.show()

Practical Example: Gradient Field

x = np.linspace(-3, 3, 15)
y = np.linspace(-3, 3, 15)
X, Y = np.meshgrid(x, y)

# Gradient of f(x,y) = x² + y²
U = 2 * X
V = 2 * Y

fig, ax = plt.subplots()

# Contours
contours = ax.contour(X, Y, X**2 + Y**2, levels=10, cmap='coolwarm')
ax.clabel(contours, inline=True, fontsize=8)

# Gradient vectors (normalized)
mag = np.sqrt(U**2 + V**2)
ax.quiver(X, Y, U/mag, V/mag, alpha=0.6)

ax.set_aspect('equal')
ax.set_title('Gradient Field')
plt.show()

Streamplot Alternative

For smoother flow visualization:

fig, ax = plt.subplots()
ax.streamplot(X, Y, U, V, density=1.5, color=magnitude, cmap='viridis')
ax.set_aspect('equal')
ax.set_title('Streamplot')
plt.show()

Common Use Cases

• Fluid flow visualization
• Electric/magnetic fields
• Wind patterns
• Gradient visualization
• Force diagrams