Create a 75-100 second cinematic 3D explainer of Morse theory through a vertically oriented torus and a rising horizontal waterline. This topic is new to our repo.
Teach an ambitious undergraduate who knows derivatives but not topology. Define sublevel sets M_a={p in T^2:h(p)<=a}, critical points, index, and Euler characteristic. Use a genuine Morse height with FOUR isolated critical points, not the degenerate height of a horizontal donut. Mathematically verify a parametrization and the four critical heights and indices before implementation. Show disk -> cylinder -> punctured torus -> closed torus as successive sublevel surfaces. Explain that the topology changes at critical levels, with Euler characteristic 1-2+1=0. Distinguish the topology of the surface sublevel set from the liquid volume and from the number of boundary curves.
Art direction: midnight blue background, luminous teal and cyan surface mesh, warm gold scanning plane, coral critical points, violet saddles. Shape and motion carry the explanation. Use ambitious but purposeful camera orbits, slow push-ins at saddles, pullbacks to restore orientation, color transitions encoding the included surface, and beautifully legible fixed on-screen LaTeX formulas. Preserve a clean hierarchy and large negative space. One main formula at a time. Use actual MathTex, 3D geometry and evolving cross-sections; no walls of text or generic slides. End with a strong view of the entire torus and the Morse relation chi(T^2)=m_0-m_1+m_2=1-2+1=0. No narration required.
Use the local Python interpreter C:/Users/chris/Math-To-Manim/.venv/Scripts/python.exe for numerical verification and Manim API inspection if needed. Installed Manim CE is 0.20.1. Research primary references where necessary. Return a complete working scene for 1920x1080 at 60fps; use efficient surfaces to keep rendering practical.Make it yours. Swap the topic in the first line ("cinematic 3D explainer of Morse theory through a vertically oriented torus") and the audience line, then rewrite the colors after "Art direction:". Replace the Windows Python path in the last paragraph with your own interpreter.
Morse theory on a torus, in 3D Manim
A silent 98-second 3D explainer: a gold plane rises through an upright torus while the surface below it goes from disk to closed torus, and four critical points explain its Euler characteristic. GPT-6 Astra wrote the Manim scene through the Codex SDK.
You'll need
- The Math-To-Manim repo, which runs the Astra and Jev chain
- A ChatGPT login for the Codex SDK
- TypeSafe Jev API access for the review checkpoints
- Manim Community Edition 0.20.1 and LaTeX
How it was made
The repo's chain runs through the Codex SDK with a ChatGPT login: GPT-6 Astra writes the learner brief, verifies the math, storyboards, writes the Manim scene, and reviews the render, while TypeSafe Jev scores each checkpoint through its own API. Jev evaluated the earlier checkpoints, then the creator stopped further model reviews to control costs. The final candidate was rendered locally with no more model calls, so the film is marked not Jev-approved. The prompt asks for 1920x1080 at 60 fps; the published film is 720p at 30 fps.
Posted Sep 24, 2026 · HarleyCoops/Math-To-Manim on GitHub · 2.7k stars
Prompt from: Production request file in the repo
Look notesby Reference
An upright torus on a midnight-blue ground, a thin teal wireframe at first and then solid cyan below a translucent horizontal plane that sits higher in each later frame, with one formula at the top and a caption at the bottom.
- Color
- Midnight navy background, a thin teal wireframe, luminous cyan and aqua shading for the included surface, a translucent gray plane with pale gold curves where it meets the surface, coral and violet dots for critical points, and white text.
- Type
- White LaTeX serif at top center ("T²: the torus surface", "dh_p = 0", "index(p) = #{negative eigenvalues of H_p}", "4 − 5 + 2 = 1") and a short white serif caption at bottom center.
- Framing
- The torus stays centered with wide empty margins, one formula above and one caption below. A triangle appears at left for the subdivision example, and a vertical index scale (0, 1, 1, 2) sits at right in the last frame.
- Sound
- Silent; the repo README calls it a silent movie.
- Structure
- The torus defined, critical points, index, a saddle at h = −1.2, the cylinder at a = 0 with two boundary curves, the band joining them at h = 1.2, the maximum at h = 2.8 capping the surface, a triangle showing subdivision preserves the count (4 − 5 + 2 = 1), and the summary "disk → cylinder → punctured torus → closed torus".
