Axes Method - hexbin¶

The ax.hexbin() method creates hexagonal binning plots for 2D data density visualization.

Basic Usage¶

Hexbin with Colorbar¶

import matplotlib.pyplot as plt
import numpy as np

def main():
    mean = [0, 0]
    cov = [[1, 1], [1, 2]]
    x = np.random.multivariate_normal(mean, cov, 10000)
    print(f"{x.shape = }")

    fig, ax = plt.subplots()
    a = ax.hexbin(x[:, 0], x[:, 1], gridsize=30, cmap='Blues')  # type(a) PolyCollection
    plt.colorbar(a, label="density")
    plt.show()

if __name__ == "__main__":
    main()

Understanding Hexbin¶

Why Hexagons?¶

Shape	Advantages
Hexagon	Equal distance to neighbors, better visual perception
Square	Simpler but diagonal neighbors are farther

Data Structure¶

import numpy as np

mean = [0, 0]
cov = [[1, 1], [1, 2]]
x = np.random.multivariate_normal(mean, cov, 10000)

print(f"Shape: {x.shape}")        # (10000, 2)
print(f"X range: [{x[:,0].min():.2f}, {x[:,0].max():.2f}]")
print(f"Y range: [{x[:,1].min():.2f}, {x[:,1].max():.2f}]")

gridsize Parameter¶

Different Grid Sizes¶

import matplotlib.pyplot as plt
import numpy as np

mean = [0, 0]
cov = [[1, 1], [1, 2]]
x = np.random.multivariate_normal(mean, cov, 10000)

fig, axes = plt.subplots(1, 4, figsize=(16, 4))
gridsizes = [10, 20, 30, 50]

for ax, gs in zip(axes, gridsizes):
    hb = ax.hexbin(x[:, 0], x[:, 1], gridsize=gs, cmap='Blues')
    ax.set_title(f'gridsize={gs}')
    fig.colorbar(hb, ax=ax, shrink=0.8)

plt.tight_layout()
plt.show()

Asymmetric Gridsize¶

import matplotlib.pyplot as plt
import numpy as np

mean = [0, 0]
cov = [[1, 1], [1, 2]]
x = np.random.multivariate_normal(mean, cov, 10000)

fig, axes = plt.subplots(1, 2, figsize=(12, 5))

# Symmetric
hb1 = axes[0].hexbin(x[:, 0], x[:, 1], gridsize=30, cmap='Blues')
axes[0].set_title('gridsize=30')
fig.colorbar(hb1, ax=axes[0])

# Asymmetric (x, y)
hb2 = axes[1].hexbin(x[:, 0], x[:, 1], gridsize=(40, 20), cmap='Blues')
axes[1].set_title('gridsize=(40, 20)')
fig.colorbar(hb2, ax=axes[1])

plt.tight_layout()
plt.show()

Colormaps¶

Different Colormaps¶

import matplotlib.pyplot as plt
import numpy as np

mean = [0, 0]
cov = [[1, 1], [1, 2]]
x = np.random.multivariate_normal(mean, cov, 10000)

fig, axes = plt.subplots(2, 3, figsize=(15, 10))
cmaps = ['Blues', 'Reds', 'Greens', 'viridis', 'plasma', 'hot']

for ax, cmap in zip(axes.flat, cmaps):
    hb = ax.hexbin(x[:, 0], x[:, 1], gridsize=30, cmap=cmap)
    ax.set_title(f"cmap='{cmap}'")
    fig.colorbar(hb, ax=ax, shrink=0.8)

plt.tight_layout()
plt.show()

Reduce Functions¶

C Parameter and reduce_C_function¶

import matplotlib.pyplot as plt
import numpy as np

# Data with associated values
n = 10000
x = np.random.randn(n)
y = np.random.randn(n)
z = x**2 + y**2  # Value at each point

fig, axes = plt.subplots(1, 3, figsize=(15, 4))

# Count (default)
hb1 = axes[0].hexbin(x, y, gridsize=20, cmap='Blues')
axes[0].set_title('Count (default)')
fig.colorbar(hb1, ax=axes[0])

# Mean of z values
hb2 = axes[1].hexbin(x, y, C=z, gridsize=20, cmap='Blues', reduce_C_function=np.mean)
axes[1].set_title('Mean of z')
fig.colorbar(hb2, ax=axes[1])

# Max of z values
hb3 = axes[2].hexbin(x, y, C=z, gridsize=20, cmap='Blues', reduce_C_function=np.max)
axes[2].set_title('Max of z')
fig.colorbar(hb3, ax=axes[2])

plt.tight_layout()
plt.show()

Minimum Count¶

mincnt Parameter¶

import matplotlib.pyplot as plt
import numpy as np

mean = [0, 0]
cov = [[1, 1], [1, 2]]
x = np.random.multivariate_normal(mean, cov, 10000)

fig, axes = plt.subplots(1, 3, figsize=(15, 4))
mincnts = [None, 5, 20]

for ax, mc in zip(axes, mincnts):
    hb = ax.hexbin(x[:, 0], x[:, 1], gridsize=30, cmap='Blues', mincnt=mc)
    ax.set_title(f'mincnt={mc}')
    fig.colorbar(hb, ax=ax, shrink=0.8)

plt.tight_layout()
plt.show()

Extent and Limits¶

Setting Data Range¶

import matplotlib.pyplot as plt
import numpy as np

mean = [0, 0]
cov = [[1, 1], [1, 2]]
x = np.random.multivariate_normal(mean, cov, 10000)

fig, axes = plt.subplots(1, 2, figsize=(12, 5))

# Auto extent
hb1 = axes[0].hexbin(x[:, 0], x[:, 1], gridsize=30, cmap='Blues')
axes[0].set_title('Auto extent')
fig.colorbar(hb1, ax=axes[0])

# Custom extent
hb2 = axes[1].hexbin(x[:, 0], x[:, 1], gridsize=30, cmap='Blues',
                     extent=[-4, 4, -6, 6])
axes[1].set_title('extent=[-4, 4, -6, 6]')
fig.colorbar(hb2, ax=axes[1])

plt.tight_layout()
plt.show()

Logarithmic Scale¶

bins='log'¶

import matplotlib.pyplot as plt
import numpy as np

mean = [0, 0]
cov = [[1, 1], [1, 2]]
x = np.random.multivariate_normal(mean, cov, 10000)

fig, axes = plt.subplots(1, 2, figsize=(12, 5))

# Linear scale
hb1 = axes[0].hexbin(x[:, 0], x[:, 1], gridsize=30, cmap='Blues')
axes[0].set_title('Linear scale')
fig.colorbar(hb1, ax=axes[0])

# Log scale
hb2 = axes[1].hexbin(x[:, 0], x[:, 1], gridsize=30, cmap='Blues', bins='log')
axes[1].set_title("bins='log'")
fig.colorbar(hb2, ax=axes[1])

plt.tight_layout()
plt.show()

Styling¶

Edge Colors and Linewidths¶

import matplotlib.pyplot as plt
import numpy as np

mean = [0, 0]
cov = [[1, 1], [1, 2]]
x = np.random.multivariate_normal(mean, cov, 10000)

fig, axes = plt.subplots(1, 3, figsize=(15, 4))

# Default
hb1 = axes[0].hexbin(x[:, 0], x[:, 1], gridsize=20, cmap='Blues')
axes[0].set_title('Default')

# With edges
hb2 = axes[1].hexbin(x[:, 0], x[:, 1], gridsize=20, cmap='Blues',
                     edgecolors='black', linewidths=0.5)
axes[1].set_title('With black edges')

# White edges
hb3 = axes[2].hexbin(x[:, 0], x[:, 1], gridsize=20, cmap='Blues',
                     edgecolors='white', linewidths=1)
axes[2].set_title('With white edges')

for ax in axes:
    fig.colorbar(ax.collections[0], ax=ax, shrink=0.8)

plt.tight_layout()
plt.show()

Return Value¶

PolyCollection Object¶

import matplotlib.pyplot as plt
import numpy as np

mean = [0, 0]
cov = [[1, 1], [1, 2]]
x = np.random.multivariate_normal(mean, cov, 10000)

fig, ax = plt.subplots()
hb = ax.hexbin(x[:, 0], x[:, 1], gridsize=30, cmap='Blues')

print(f"Type: {type(hb)}")  # PolyCollection
print(f"Array shape: {hb.get_array().shape}")  # Counts per hexagon

plt.colorbar(hb, label='counts')
plt.show()

Practical Example¶

Density Analysis¶

import matplotlib.pyplot as plt
import numpy as np

# Generate bimodal data
np.random.seed(42)
n = 5000
x1 = np.random.multivariate_normal([0, 0], [[1, 0.5], [0.5, 1]], n)
x2 = np.random.multivariate_normal([3, 3], [[1, -0.5], [-0.5, 1]], n)
x = np.vstack([x1, x2])

fig, ax = plt.subplots(figsize=(10, 8))

hb = ax.hexbin(x[:, 0], x[:, 1], gridsize=35, cmap='YlOrRd', 
               edgecolors='white', linewidths=0.2)

ax.set_xlabel('X', fontsize=12)
ax.set_ylabel('Y', fontsize=12)
ax.set_title('Bimodal Distribution Density', fontsize=14)

cbar = fig.colorbar(hb, ax=ax, label='Point Count')
plt.tight_layout()
plt.show()