Math — Plotting

A progressive study of data visualization with Matplotlib — from basic line plots to 3D PCA, covering line graphs, scatter plots, histograms, bar charts, subplots, color mapping, and dimensionality reduction.

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Learning Objectives

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Task-by-Task Reference

Each task below highlights the unique challenge it posed and the new technique introduced — techniques from earlier tasks are not repeated.

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Task 0 — Line Plot (0-line.py)

Challenge: Create a basic line graph — the simplest possible visualization, introducing the Matplotlib plotting pipeline.

Approach: Generate y-values as the cube of 0–10 using NumPy, then call plt.plot(y, color='r') to draw a red line. Set x-axis limits with plt.xlim().

New techniques introduced:

Key takeaway: plt.plot() is the universal line-plotting function. The color parameter accepts named colors ('r'), hex codes, or RGB tuples. plt.show() renders everything — without it, no plot appears.

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Task 1 — Scatter Plot (1-scatter.py)

Challenge: Create a labeled scatter plot from bivariate normal data — introducing axis labels, titles, and scatter-specific styling.

Approach: Generate 2000 points from a multivariate normal distribution with np.random.multivariate_normal(). Use plt.scatter(x, y, c='magenta') for colored points. Add labels and title with plt.xlabel(), plt.ylabel(), plt.title().

New techniques introduced:

Key takeaway: plt.scatter() is ideal for showing relationships between two variables. Unlike plt.plot(), it doesn't connect points — each marker stands alone. Always label your axes for interpretable visualizations.

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Task 2 — Logarithmic Scale (2-change_scale.py)

Challenge: Visualize exponential decay data where values span multiple orders of magnitude — introducing logarithmic axis scaling.

Approach: Model Carbon-14 decay as $y = e^{(\ln 0.5 / 5730) \cdot x}$ for $x$ from 0 to 28,650 years. Apply plt.yscale("log") to compress the y-axis, making the exponential curve appear linear — a classic diagnostic for exponential processes.

New techniques introduced:

Key takeaway: Logarithmic scales make exponential relationships visually linear — a straight line on a log plot confirms exponential behavior. Use plt.yscale("log") or plt.xscale("log") when data spans multiple orders of magnitude.

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Task 3 — Two Curves with Legend (3-two.py)

Challenge: Compare two radioactive decay curves (C-14 and Ra-226) on the same plot — introducing multiple line styles, legends, and axis range control.

Approach: Plot C-14 with a red dashed line (linestyle="--") and Ra-226 with a green solid line. Use label= on each plt.plot() call, then plt.legend(loc="upper right") to identify the curves. Set both x and y limits with plt.xlim() and plt.ylim().

New techniques introduced:

Key takeaway: When plotting multiple curves, always add a legend. The label parameter in plt.plot() pairs with plt.legend() to identify each curve. Line styles (solid, dashed, dotted) provide redundancy for colorblind accessibility.

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Task 4 — Histogram (4-frequency.py)

Challenge: Visualize the distribution of student grades — introducing histograms with custom bin edges and styling.

Approach: Generate 50 random grades from $\mathcal{N}(68, 15)$. Define bins every 10 units (0–100) with np.arange(). Call plt.hist() with bins=bins and edgecolor='black' for outlined bars. Set x-ticks to match bin edges.

New techniques introduced:

Key takeaway: Histograms reveal the shape of data distributions (normal, skewed, bimodal). The bins parameter controls granularity — too few bins hide detail, too many create noise. edgecolor makes individual bars distinguishable.

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Task 5 — Subplot Grid (5-all_in_one.py)

Challenge: Combine all five previous plots into a single figure — introducing Matplotlib's subplot grid system and figure-level titling.

Approach: Create a 3×2 grid of subplots using plt.subplot(3, 2, i). The last plot spans two columns using plt.subplot2grid(). Set all font sizes to x-small with plt.rcParams. Add a figure-level title with plt.suptitle() and adjust spacing with plt.tight_layout().

New techniques introduced:

Key takeaway: Subplots let you compare multiple visualizations side by side. plt.subplot() uses 1-based indexing. For complex layouts, subplot2grid() gives fine-grained control over cell spanning.

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Task 6 — Stacked Bar Chart (6-bars.py)

Challenge: Display categorical data as stacked bars — introducing bar charts, custom colors, and categorical tick labels.

Approach: Use plt.bar() with bottom= parameter to stack fruit quantities per person. Assign specific colors (apples=red, bananas=yellow, oranges=#ff8000, peaches=#ffe5b4). Add a legend, set bar width to 0.5, and use plt.xticks() with person names.

New techniques introduced:

Key takeaway: Stacked bar charts show both individual contributions and totals. The bottom parameter stacks bars by specifying where each segment starts. Custom hex colors and legends make categorical data readable.

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Task 7 — Gradient Scatter (100-gradient.py)

Challenge: Add a third dimension (elevation) to a scatter plot using color — introducing colorbars for continuous data mapping.

Approach: Generate random x, y coordinates and compute elevation $z = 40 - \sqrt{x^2 + y^2} + \text{noise}$. Pass c=z to plt.scatter() to color points by elevation. Add plt.colorbar(label="elevation (m)") for a reference scale.

New techniques introduced:

Key takeaway: Color adds a third dimension to 2D scatter plots. The c parameter accepts any numeric array — Matplotlib automatically normalizes and maps values to a colormap. Always include a colorbar to make the scale interpretable.

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Task 8 — 3D PCA Visualization (101-pca.py)

Challenge: Visualize 4-dimensional Iris flower data in 3D — introducing PCA dimensionality reduction and 3D plotting.

Approach: Load the Iris dataset, center the data by subtracting means, compute SVD to get principal components, then project onto the top 3 components. Use Axes3D for 3D scatter with cmap='plasma' coloring by species label.

New techniques introduced:

Key takeaway: PCA reduces high-dimensional data to its most informative dimensions. SVD is the computational engine — it finds the directions of maximum variance. 3D plots let you inspect the reduced space interactively. PCA is essential for both visualization and preprocessing.

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Technique Inventory

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Resources

• Matplotlib Pyplot Tutorial
• Matplotlib Colors API
• NumPy SVD Documentation
• PCA Explained — towardsdatascience
• Iris Dataset — Wikipedia