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Manim Visualizations for Physics & Math

Manim Visualizations for Physics & Math

Educational Visualization

Programmatic animations using Manim to explain math/physics concepts through code-defined scenes.

GitHub Repo

Problem

Static diagrams don’t convey dynamic phenomena well; editing animations by hand is slow and hard to reproduce.

Solution

I scripted Manim scenes so animations are reproducible, tweakable, and faithful to the underlying math.

What I Did

  • Structured the repo for repeatable animation work

    • Split scenes into focused modules (e.g., scenes/linear_algebra.py, scenes/calculus.py, scenes/physics.py).
    • Shared helpers for colors, fonts, axes, and labels (e.g., utils/axes.py, utils/labels.py) so scenes stay short and consistent.
    • Standardized export settings (16:9, 1080p) and output names to keep assets organized for reuse in slides.

  • Built a library of short, pedagogical animations (examples)

    • Linear algebra / transforms: animate basis vectors, visualize matrix effects (rotation (R_\theta), shear), area scaling via (|\det A|), and eigenvectors/eigenvalues as invariant directions.
    • Calculus: Riemann sums morphing into integrals, tangent as the limit of secants, and parametric curve motion driven by a single time parameter.
    • Classical mechanics: mass–spring oscillator with a ValueTracker showing live energy bars; projectile motion with vector decomposition and trajectories under different launch angles.
    • Chaos / dynamics (optional): logistic map iterations and phase portraits using always_redraw updaters for responsive traces.
    • Fourier intuition (optional): partial sums and epicycle-style phasor drawings to converge to a target curve or signal.

  • Manim techniques & patterns I used repeatedly

    • MathTex / Tex for crisp equations; consistent font size/baselines for overlays on graphs.
    • Updaters & ValueTracker for time-dependent geometry (sliders, “live” labels, energy bars, error metrics).
    • Axes / NumberPlane / Vector fields to ground visuals; custom tick/label formatting for scientific units.
    • Core animations: Create, Write, Transform, ReplacementTransform, FadeIn/FadeOut, with tuned run_time and lag_ratio for pacing.
    • Camera control via MovingCameraScene (zoom/follow a mobject) and simple 3D camera sweeps when depth helps.
    • Exported both MP4 and lightweight GIF versions for web embedding and slide decks.

  • Performance & quality

    • Used caching where appropriate; precomputed slow backgrounds; kept scenes modular to render independently.
    • Chose quality flags intentionally: -pqh for quick previews, -p --quality=high / -p --quality=uhd for finals.
    • Pinned Manim CE version in requirements to keep outputs stable across machines.

Preview

  • Preview a single scene (quick): Three-Body Diagram Simple three-body diagram.