Limits and Ticks¶

Control the visible range and tick positions on your axes.

Setting Axis Limits¶

Use set_xlim and set_ylim:

```python import matplotlib.pyplot as plt import numpy as np

x = np.linspace(-2np.pi, 2np.pi, 100) y = np.sin(x)

fig, ax = plt.subplots(figsize=(12, 3)) ax.plot(x, y) ax.set_xlim((-3np.pi, 3np.pi)) ax.set_ylim((-2, 2)) plt.show() ```

Getting Current Limits¶

python print(ax.get_xlim()) # Returns tuple: (-9.42..., 9.42...) print(ax.get_ylim()) # Returns tuple: (-2.0, 2.0)

Setting Ticks¶

Use set_xticks and set_yticks:

```python import matplotlib.pyplot as plt import numpy as np

x = np.linspace(-2np.pi, 2np.pi, 100) y = np.sin(x)

fig, ax = plt.subplots(figsize=(12, 3)) ax.plot(x, y) ax.set_yticks(ticks=[-1, 0, 1]) ax.set_xticks(ticks=[-2np.pi, -np.pi, 0, np.pi, 2np.pi]) plt.show() ```

Removing Ticks¶

Pass an empty tuple to remove all ticks:

```python import matplotlib.pyplot as plt import numpy as np

x = np.linspace(-2np.pi, 2np.pi, 100) y = np.sin(x)

fig, ax = plt.subplots(figsize=(12, 3)) ax.plot(x, y) ax.set_xticks(()) ax.set_yticks(()) plt.show() ```

Tick Labels¶

Set custom labels with the labels parameter:

```python import matplotlib.pyplot as plt import numpy as np

x = np.linspace(-2np.pi, 2np.pi, 100) y = np.sin(x)

fig, ax = plt.subplots(figsize=(12, 3)) ax.plot(x, y) ax.set_yticks(ticks=[-1, 0, 1]) ax.set_xticks( ticks=[-2np.pi, -np.pi, 0, np.pi, 2np.pi], labels=["\(-2\\pi\)", "\(-\\pi\)", "0", "\(\\pi\)", "\(2\\pi\)"] ) plt.show() ```

Minor Ticks¶

Add minor ticks with minor=True:

```python import matplotlib.pyplot as plt import numpy as np

x = np.linspace(-2np.pi, 2np.pi, 100) y = np.sin(x)

fig, ax = plt.subplots(figsize=(12, 3)) ax.plot(x, y)

Major ticks¶

ax.set_yticks(ticks=[-1, 0, 1]) ax.set_xticks( ticks=[-2np.pi, -np.pi, 0, np.pi, 2np.pi], labels=["\(-2\\pi\)", "\(-\\pi\)", "0", "\(\\pi\)", "\(2\\pi\)"] )

Minor ticks (no labels)¶

ax.set_xticks( ticks=np.linspace(-2np.pi, 2np.pi, 17), labels=[], minor=True )

plt.show() ```

Getting Current Ticks¶

python print(ax.get_xticks()) print(ax.get_yticks())

Complete Example with Spines¶

```python import matplotlib.pyplot as plt import numpy as np

x = np.linspace(-2np.pi, 2np.pi, 100) y = np.sin(x)

fig, ax = plt.subplots(figsize=(12, 3)) ax.plot(x, y)

Set ticks and labels¶

ax.set_yticks(ticks=[-1, 0, 1]) ax.set_xticks( ticks=[-2np.pi, -np.pi, 0, np.pi, 2np.pi], labels=["\(-2\\pi\)", "\(-\\pi\)", "0", "\(\\pi\)", "\(2\\pi\)"] ) ax.set_xticks( ticks=np.linspace(-2np.pi, 2np.pi, 17), labels=[], minor=True )

Move spines to origin¶

ax.spines['top'].set_visible(False) ax.spines['right'].set_visible(False) ax.spines['bottom'].set_position('zero') ax.spines['left'].set_position('zero')

plt.show() ```

tick_params¶

Fine-tune tick appearance:

python ax.tick_params( axis='both', # 'x', 'y', or 'both' which='major', # 'major', 'minor', or 'both' direction='out', # 'in', 'out', or 'inout' length=6, # Tick length width=2, # Tick width labelsize=10, # Label font size rotation=45, # Label rotation colors='blue' # Tick and label color )

Key Takeaways¶

• set_xlim() and set_ylim() control visible range
• set_xticks() and set_yticks() set tick positions
• Use labels parameter for custom tick labels
• Use minor=True for minor ticks
• tick_params() provides fine-grained control
• Empty tuple () removes all ticks

Runnable Example: advanced_customization_tutorial.py¶

```python """ Matplotlib Tutorial - Intermediate Level ======================================== Topic: Advanced Plot Customization and Styling Author: Educational Python Course Level: Intermediate

Learning Objectives:¶

1. Master axes limits and ticks customization
2. Understand different coordinate systems
3. Add annotations and text
4. Customize grids and spines
5. Control legend appearance and positioning
6. Use colormaps effectively
7. Create publication-quality figures

Prerequisites:¶

• Completion of beginner tutorials
• Completion of plot() and hist() guides """

import matplotlib.pyplot as plt import numpy as np

============================================================================¶

SECTION 1: Customizing Axes Limits¶

============================================================================¶

if name == "main":

"""
Controlling what portion of data is visible
"""

x = np.linspace(0, 10, 100)
y = np.sin(x)

fig, axes = plt.subplots(2, 2, figsize=(12, 10))

# Default limits (automatic)
axes[0, 0].plot(x, y)
axes[0, 0].set_title('Default limits (automatic)')
axes[0, 0].grid(True, alpha=0.3)

# Custom x-limits only
axes[0, 1].plot(x, y)
axes[0, 1].set_xlim(2, 8)  # Show only x from 2 to 8
axes[0, 1].set_title('Custom xlim(2, 8)')
axes[0, 1].grid(True, alpha=0.3)

# Custom y-limits only
axes[1, 0].plot(x, y)
axes[1, 0].set_ylim(-2, 2)  # Extend y-axis range
axes[1, 0].set_title('Custom ylim(-2, 2)')
axes[1, 0].grid(True, alpha=0.3)

# Both custom limits
axes[1, 1].plot(x, y)
axes[1, 1].set_xlim(3, 7)
axes[1, 1].set_ylim(-0.5, 0.5)
axes[1, 1].set_title('Custom xlim and ylim')
axes[1, 1].grid(True, alpha=0.3)

plt.tight_layout()
plt.show()

# ============================================================================
# SECTION 2: Customizing Ticks and Tick Labels
# ============================================================================

"""
Ticks are the marks on the axes.
Tick labels are the text at each tick.
"""

x = np.linspace(0, 10, 100)
y = np.sin(x)

fig, axes = plt.subplots(2, 2, figsize=(12, 10))

# Default ticks
axes[0, 0].plot(x, y)
axes[0, 0].set_title('Default ticks')
axes[0, 0].grid(True, alpha=0.3)

# Custom tick positions
axes[0, 1].plot(x, y)
axes[0, 1].set_xticks([0, 2, 4, 6, 8, 10])  # Specific positions
axes[0, 1].set_yticks([-1, -0.5, 0, 0.5, 1])
axes[0, 1].set_title('Custom tick positions')
axes[0, 1].grid(True, alpha=0.3)

# Custom tick labels (different from positions)
axes[1, 0].plot(x, y)
axes[1, 0].set_xticks([0, np.pi, 2*np.pi, 3*np.pi])
axes[1, 0].set_xticklabels(['0', 'π', '2π', '3π'])
axes[1, 0].set_title('Custom tick labels')
axes[1, 0].grid(True, alpha=0.3)

# Rotated and formatted labels
axes[1, 1].plot(x, y)
axes[1, 1].set_xticks(np.arange(0, 11, 1))
axes[1, 1].set_xticklabels([f'x={i}' for i in range(11)], rotation=45, ha='right')
axes[1, 1].set_title('Rotated tick labels')
axes[1, 1].grid(True, alpha=0.3)

plt.tight_layout()
plt.show()

# ============================================================================
# SECTION 3: Grid Customization
# ============================================================================

"""
Grids help read values from plots
"""

x = np.linspace(0, 10, 100)
y = np.sin(x)

fig, axes = plt.subplots(2, 3, figsize=(15, 10))

# No grid
axes[0, 0].plot(x, y)
axes[0, 0].set_title('No grid')

# Basic grid
axes[0, 1].plot(x, y)
axes[0, 1].grid(True)
axes[0, 1].set_title('Basic grid')

# Customized grid (color, style, width)
axes[0, 2].plot(x, y)
axes[0, 2].grid(True, color='red', linestyle='--', linewidth=0.5, alpha=0.7)
axes[0, 2].set_title('Customized grid')

# Grid only on y-axis
axes[1, 0].plot(x, y)
axes[1, 0].grid(True, axis='y', alpha=0.5)
axes[1, 0].set_title('Grid on y-axis only')

# Grid with minor ticks
axes[1, 1].plot(x, y)
axes[1, 1].minorticks_on()
axes[1, 1].grid(True, which='major', linestyle='-', linewidth=0.8, alpha=0.7)
axes[1, 1].grid(True, which='minor', linestyle=':', linewidth=0.5, alpha=0.4)
axes[1, 1].set_title('Major and minor grids')

# Grid behind plot
axes[1, 2].plot(x, y, linewidth=3, zorder=3)  # zorder=3 brings line to front
axes[1, 2].grid(True, zorder=0, alpha=0.5)  # zorder=0 puts grid in back
axes[1, 2].set_title('Grid behind line (zorder)')

plt.tight_layout()
plt.show()

# ============================================================================
# SECTION 4: Spine Customization
# ============================================================================

"""
Spines are the lines connecting the axis tick marks and noting the boundaries of the data area.
There are 4 spines: 'left', 'right', 'top', 'bottom'
"""

x = np.linspace(-5, 5, 100)
y = x ** 2

fig, axes = plt.subplots(2, 2, figsize=(12, 10))

# All spines visible (default)
axes[0, 0].plot(x, y)
axes[0, 0].set_title('All spines (default)')

# Hide top and right spines (common for scientific plots)
axes[0, 1].plot(x, y)
axes[0, 1].spines['top'].set_visible(False)
axes[0, 1].spines['right'].set_visible(False)
axes[0, 1].set_title('Top and right spines hidden')

# Customize spine position (centered at zero)
axes[1, 0].plot(x, y)
axes[1, 0].spines['left'].set_position('zero')  # Move left spine to x=0
axes[1, 0].spines['bottom'].set_position('zero')  # Move bottom spine to y=0
axes[1, 0].spines['top'].set_visible(False)
axes[1, 0].spines['right'].set_visible(False)
axes[1, 0].set_title('Spines at zero (classic math axes)')

# Customize spine colors and linewidth
axes[1, 1].plot(x, y)
for spine in axes[1, 1].spines.values():
    spine.set_edgecolor('red')
    spine.set_linewidth(2)
axes[1, 1].set_title('Custom spine color and width')

plt.tight_layout()
plt.show()

# ============================================================================
# SECTION 5: Adding Text and Annotations
# ============================================================================

"""
Text and annotations help explain features in plots
"""

x = np.linspace(0, 10, 100)
y = np.sin(x)

fig, ax = plt.subplots(figsize=(12, 6))
ax.plot(x, y, 'b-', linewidth=2)

# Simple text at data coordinates
ax.text(5, 0.5, 'Simple text', fontsize=14)

# Text with background box
ax.text(8, -0.5, 'Text with box', fontsize=12,
        bbox=dict(boxstyle='round', facecolor='wheat', alpha=0.5))

# Annotation with arrow pointing to data
ax.annotate('Local maximum', 
            xy=(np.pi/2, 1),  # Point to annotate
            xytext=(2, 1.3),  # Text position
            fontsize=12,
            arrowprops=dict(arrowstyle='->', color='red', lw=2),
            bbox=dict(boxstyle='round', facecolor='yellow', alpha=0.7))

# Another annotation
ax.annotate('Zero crossing',
            xy=(np.pi, 0),
            xytext=(4, -0.5),
            fontsize=12,
            arrowprops=dict(arrowstyle='->', color='green', lw=2))

ax.set_xlabel('x', fontsize=14)
ax.set_ylabel('sin(x)', fontsize=14)
ax.set_title('Adding Text and Annotations', fontsize=16)
ax.grid(True, alpha=0.3)

plt.show()

# ============================================================================
# SECTION 6: Advanced Legend Customization
# ============================================================================

"""
Legends explain what each line/marker represents
"""

x = np.linspace(0, 10, 100)

fig, axes = plt.subplots(2, 2, figsize=(12, 10))

# Different legend locations
for i, loc in enumerate(['upper right', 'upper left', 'lower left', 'best']):
    ax = axes[i // 2, i % 2]
    ax.plot(x, np.sin(x), 'r-', label='sin(x)')
    ax.plot(x, np.cos(x), 'b--', label='cos(x)')
    ax.plot(x, np.sin(2*x), 'g:', label='sin(2x)')
    ax.legend(loc=loc)
    ax.set_title(f"loc='{loc}'")
    ax.grid(True, alpha=0.3)

plt.tight_layout()
plt.show()

# Highly customized legend
fig, ax = plt.subplots(figsize=(10, 6))

ax.plot(x, np.sin(x), 'r-', linewidth=2, label='sin(x)')
ax.plot(x, np.cos(x), 'b--', linewidth=2, label='cos(x)')
ax.plot(x, np.tan(x), 'g:', linewidth=2, label='tan(x)')

ax.legend(
    loc='upper right',
    fontsize=12,
    frameon=True,          # Draw frame
    framealpha=0.9,        # Frame transparency
    shadow=True,           # Add shadow
    fancybox=True,         # Rounded corners
    title='Functions',     # Legend title
    title_fontsize=14
)

ax.set_ylim(-3, 3)
ax.set_title('Customized Legend', fontsize=16)
ax.grid(True, alpha=0.3)

plt.show()

# ============================================================================
# SECTION 7: Colormaps for Multiple Lines
# ============================================================================

"""
When plotting many lines, colormaps provide systematic colors
"""

x = np.linspace(0, 10, 100)

fig, axes = plt.subplots(1, 2, figsize=(14, 5))

# Manual colors (tedious for many lines)
colors = ['red', 'blue', 'green', 'orange', 'purple']
for i, color in enumerate(colors):
    axes[0].plot(x, np.sin(x + i*0.5), color=color, label=f'Line {i}')
axes[0].set_title('Manual colors')
axes[0].legend()

# Using colormap (systematic and scalable)
n_lines = 10
colormap = plt.cm.viridis  # Choose a colormap
colors = [colormap(i / n_lines) for i in range(n_lines)]

for i, color in enumerate(colors):
    axes[1].plot(x, np.sin(x + i*0.3), color=color, label=f'Line {i}')

axes[1].set_title('Using colormap (viridis)')
axes[1].legend()

plt.tight_layout()
plt.show()

# ============================================================================
# SECTION 8: Figure Size and DPI
# ============================================================================

"""
Control figure dimensions and resolution
"""

x = np.linspace(0, 10, 100)
y = np.sin(x)

# Small figure, low DPI
fig1, ax1 = plt.subplots(figsize=(4, 3), dpi=50)
ax1.plot(x, y)
ax1.set_title('4"×3", 50 DPI (looks pixelated)')
plt.show()

# Large figure, high DPI
fig2, ax2 = plt.subplots(figsize=(10, 6), dpi=150)
ax2.plot(x, y, linewidth=2)
ax2.set_xlabel('x', fontsize=14)
ax2.set_ylabel('sin(x)', fontsize=14)
ax2.set_title('10"×6", 150 DPI (sharp and clear)', fontsize=16)
ax2.grid(True, alpha=0.3)
plt.show()

print("Figure size = (width, height) in inches")
print("DPI = dots per inch (resolution)")
print("Pixel dimensions = (width × DPI, height × DPI)")
print("Example: (10, 6) at 150 DPI = 1500×900 pixels")

# ============================================================================
# SECTION 9: Publication-Quality Figure Example
# ============================================================================

"""
Combining everything for a professional-looking plot
"""

# Generate data
x = np.linspace(0, 10, 200)
y1 = np.sin(x)
y2 = np.sin(x) * np.exp(-x/5)
y3 = np.cos(x) * np.exp(-x/5)

# Create figure with specific size and DPI
fig, ax = plt.subplots(figsize=(10, 6), dpi=120)

# Plot with careful styling
line1, = ax.plot(x, y1, color='#1f77b4', linestyle='-', linewidth=2.5, 
                 label='sin(x)', alpha=0.9)
line2, = ax.plot(x, y2, color='#ff7f0e', linestyle='--', linewidth=2.5,
                 label='sin(x)·exp(-x/5)', alpha=0.9)
line3, = ax.plot(x, y3, color='#2ca02c', linestyle='-.', linewidth=2.5,
                 label='cos(x)·exp(-x/5)', alpha=0.9)

# Customize axes
ax.set_xlabel('x', fontsize=14, fontweight='bold')
ax.set_ylabel('y', fontsize=14, fontweight='bold')
ax.set_title('Damped Oscillations', fontsize=16, fontweight='bold', pad=20)

# Set limits
ax.set_xlim(0, 10)
ax.set_ylim(-1.2, 1.2)

# Customize ticks
ax.tick_params(axis='both', which='major', labelsize=12, length=6, width=1.5)
ax.minorticks_on()
ax.tick_params(axis='both', which='minor', length=3, width=1)

# Grid
ax.grid(True, which='major', linestyle='-', linewidth=0.8, alpha=0.3)
ax.grid(True, which='minor', linestyle=':', linewidth=0.5, alpha=0.2)

# Customize spines
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)
ax.spines['left'].set_linewidth(1.5)
ax.spines['bottom'].set_linewidth(1.5)

# Legend
ax.legend(loc='upper right', fontsize=12, framealpha=0.9, 
          shadow=True, fancybox=True)

# Tight layout to prevent label cutoff
plt.tight_layout()

plt.show()

# ============================================================================
# KEY TAKEAWAYS
# ============================================================================

"""
1. Axes limits: set_xlim(), set_ylim()
2. Ticks: set_xticks(), set_yticks(), set_xticklabels(), set_yticklabels()
3. Grid: grid(True/False), customize with color, linestyle, linewidth, alpha
4. Spines: 4 spines (top, bottom, left, right), can hide or reposition
5. Text: text() for simple text, annotate() for text with arrows
6. Legend: customize location, frame, font, shadow
7. Colormaps: systematic colors for many lines
8. Figure size: figsize=(width, height) in inches
9. DPI: resolution (dots per inch), higher = sharper
10. Publication quality: careful attention to all visual elements

Common Customization Workflow:
-----------------------------
1. Plot data with clear line styles
2. Add labels (xlabel, ylabel, title) with appropriate font sizes
3. Set limits if needed
4. Add grid with alpha < 0.5 for subtlety
5. Hide top/right spines for cleaner look
6. Add legend with framealpha and shadow
7. Set figure size and DPI for intended output
8. Use tight_layout() to prevent cutoff
9. Save with savefig() before show()
"""

```

Exercises¶

Exercise 1. Plot y = sin(x) over \([0, 4\pi]\). Set the x-axis ticks at multiples of \(\pi\) (0, \(\pi\), \(2\pi\), \(3\pi\), \(4\pi\)) with labels showing the \(\pi\) symbol. Set the y-axis limits to \([-1.5, 1.5]\) with ticks at \([-1, -0.5, 0, 0.5, 1]\).

import matplotlib.pyplot as plt
import numpy as np

x = np.linspace(0, 4 * np.pi, 500)
y = np.sin(x)

fig, ax = plt.subplots(figsize=(10, 5))
ax.plot(x, y)

ax.set_xticks([0, np.pi, 2*np.pi, 3*np.pi, 4*np.pi])
ax.set_xticklabels([r'$0$', r'$\pi$', r'$2\pi$', r'$3\pi$', r'$4\pi$'])
ax.set_ylim(-1.5, 1.5)
ax.set_yticks([-1, -0.5, 0, 0.5, 1])

ax.set_title(r'$y = \sin(x)$ with $\pi$ Tick Labels')
plt.show()

Exercise 2. Create a scatter plot of 200 random points. Set the x-limits to [0, 1] and y-limits to [0, 1] regardless of the data range. Add ticks at every 0.1 increment and rotate the x-tick labels by 45 degrees. Also set minor ticks at every 0.05 increment.

import matplotlib.pyplot as plt
import numpy as np
from matplotlib.ticker import MultipleLocator

np.random.seed(42)
x = np.random.rand(200)
y = np.random.rand(200)

fig, ax = plt.subplots(figsize=(7, 7))
ax.scatter(x, y, alpha=0.5, s=20)
ax.set_xlim(0, 1)
ax.set_ylim(0, 1)

ax.xaxis.set_major_locator(MultipleLocator(0.1))
ax.yaxis.set_major_locator(MultipleLocator(0.1))
ax.xaxis.set_minor_locator(MultipleLocator(0.05))
ax.yaxis.set_minor_locator(MultipleLocator(0.05))

ax.tick_params(axis='x', rotation=45)
ax.set_title('Scatter with Fine Ticks')
plt.show()

Exercise 3. Plot three subplots (1x3) of the same data y = x^3 - 3*x over \([-3, 3]\): the first with default limits, the second zoomed into the region \([-1, 1] \times [-2, 2]\), and the third zoomed into \([1, 3] \times [0, 20]\). Add titles indicating the zoom region for each.

import matplotlib.pyplot as plt
import numpy as np

x = np.linspace(-3, 3, 500)
y = x**3 - 3*x

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

axes[0].plot(x, y, color='navy')
axes[0].set_title('Full View (default)')

axes[1].plot(x, y, color='navy')
axes[1].set_xlim(-1, 1)
axes[1].set_ylim(-2, 2)
axes[1].set_title('Zoom: [-1,1] x [-2,2]')

axes[2].plot(x, y, color='navy')
axes[2].set_xlim(1, 3)
axes[2].set_ylim(0, 20)
axes[2].set_title('Zoom: [1,3] x [0,20]')

for ax in axes:
    ax.grid(True, alpha=0.3)

plt.tight_layout()
plt.show()

Exercise 4. Demonstrate how axis limits "change the story." Plot y = sin(x) over [0, 4π] three ways: (a) full range, (b) zoomed to one period [0, 2π], (c) zoomed to a narrow region [π-0.5, π+0.5] with y-limits [-0.5, 0.5]. Explain how each view reveals or hides different aspects of the function.

import matplotlib.pyplot as plt
import numpy as np

x = np.linspace(0, 4 * np.pi, 500)
y = np.sin(x)

fig, axes = plt.subplots(1, 3, figsize=(14, 4))

axes[0].plot(x, y)
axes[0].set_title('Full range: periodic pattern')

axes[1].plot(x, y)
axes[1].set_xlim(0, 2 * np.pi)
axes[1].set_title('One period: shape detail')

axes[2].plot(x, y)
axes[2].set_xlim(np.pi - 0.5, np.pi + 0.5)
axes[2].set_ylim(-0.5, 0.5)
axes[2].set_title('Narrow zoom: near-linear')

plt.tight_layout()
plt.show()

# (a) reveals periodicity — you see the repeating pattern
# (b) reveals shape — the full wave is visible in detail
# (c) hides periodicity entirely — sin(x) looks linear near π