Scientific Visualization Scientific¶

What you'll learn¶

• Why visualization matters in science
• The Matplotlib workflow
• Choosing the right plot type
• 3D and volume rendering
• Interactive and domain-specific tools

A plot turns numbers into understanding. Scientific visualization is how researchers explore data, verify simulations, and communicate results. Python's ecosystem — anchored by Matplotlib — covers everything from a quick line chart to interactive 3D.

Why it matters¶

A core question explored in Scientific Visualization: Why it matters.

Numbers alone hide patterns. A visualization reveals trends, outliers, and structure the eye catches instantly. In science specifically, plots:

• Explore — spot the shape of data before formal analysis.
• Verify — does the simulation output look physically sensible?
• Communicate — a figure conveys a result faster than a table.

Anscombe's quartet is the classic lesson: four datasets with identical summary statistics look completely different when plotted. Always plot your data.

The Matplotlib workflow¶

Build figures with the object-oriented API for reproducible scientific plots.

Matplotlib is the foundation. The standard pattern — figure, axes, plot, label:

import matplotlib.pyplot as plt   # pip install matplotlib
import numpy as np

x = np.linspace(0, 2 * np.pi, 100)

fig, ax = plt.subplots()
ax.plot(x, np.sin(x), label="sin")
ax.plot(x, np.cos(x), label="cos")
ax.set_xlabel("x")
ax.set_ylabel("y")
ax.set_title("Trig functions")
ax.legend()
fig.savefig("plot.png", dpi=150)     # or plt.show() for a window

The fig, ax = plt.subplots() pattern (explicit figure and axes objects) is the recommended modern style — clearer and more controllable than the older stateful plt.plot() calls.

Choosing the right plot¶

Match the chart to the data — fields, distributions, time series, 3D.

Match the plot to the data and question:

The wrong plot obscures; the right one reveals. A common scientific mistake is a bar chart where a scatter or box plot would show the real distribution.

3D and volume rendering¶

Visualize volumetric and surface data with mplot3d/Mayavi/PyVista.

For 3D data — surfaces, fields, molecular structures:

• Matplotlib mplot3d — basic 3D surfaces and scatter; fine for figures, not interactivity.
• Mayavi / PyVista — serious 3D scientific visualization (volumes, isosurfaces, meshes).
• VTK — the underlying toolkit for heavy 3D/volume rendering.

from mpl_toolkits.mplot3d import Axes3D
import numpy as np, matplotlib.pyplot as plt

x = y = np.linspace(-5, 5, 50)
X, Y = np.meshgrid(x, y)
Z = np.sin(np.sqrt(X**2 + Y**2))     # a ripple surface

fig = plt.figure()
ax = fig.add_subplot(projection="3d")
ax.plot_surface(X, Y, Z, cmap="viridis")

Interactive & domain-specific tools¶

Plotly, Bokeh, and field-specific viewers for exploration.

• Plotly / Bokeh — interactive, web-based plots (zoom, hover, pan) — great for exploration and dashboards.
• HoloViews — high-level interactive viz that reduces boilerplate.
• Seaborn — statistical plots on top of Matplotlib (see the Data & AI section).
• Domain-specific — Biopython for phylogenetic trees, GeoPandas/Folium for maps (GIS), specialized tools per field.

Practice exercises¶

1. Plot the output of the tested ODE integrator — the decay curve y = e⁻ᵗ vs your Euler approximation.
2. Visualize the tested Monte Carlo π — scatter the random points, coloring inside/outside the circle.
3. Make a histogram of 10,000 samples from random.gauss and confirm the bell shape.
4. Plot the gradient descent path descending toward the minimum.
5. Explain why viridis is a better default colormap than jet (perceptual uniformity).