Three-body problem simulator in ~1,000 lines of Bend2 with formally proven program laws ("Fable 5.5", one shot, X video)

Summary
This video presents a screen recording of a real-time, interactive three-body problem gravitational simulator running in a macOS desktop window. Reportedly generated one-shot by an AI model ("Fable 5.5") in approximately 1,000 lines of Bend2 code with formally verified program laws, the demonstration executes an automated "tour" cycling through 10 canonical three-body orbital solutions and chaotic configurations.

What is shown

• UI & HUD: A dark-mode window titled 3 Corpos displaying the current preset name, real-time performance (60 FPS), simulation time t, energy drift dE/E in parts-per-million (ppm), simulation speed multiplier, and dynamic equipotential contour lines representing the gravitational field.
• [00:00 - 00:08] Preset 1/10: Figura-8 (Moore, Chenciner-Montgomery) — Three bodies of equal mass traversing a shared figure-8 choreographic trajectory with near-zero energy error (dE/E = 0 ppm).
• [00:09 - 00:15] Preset 2/10: Borboleta (Suvakov-Dmitrasinovic) — The periodic "Butterfly" planar three-body choreography.
• [00:16 - 00:23] Preset 3/10: Mariposa (Suvakov-Dmitrasinovic) — The intricate periodic "Moth/Mariposa" three-body orbit.
• [00:24 - 00:33] Preset 4/10: Yin-Yang (Suvakov-Dmitrasinovic) — A periodic interlaced orbit named after the yin-yang motif.
• [00:34 - 00:44] Preset 5/10: Novelo (Suvakov-Dmitrasinovic) — The tightly wound "Yarn ball" (Novelo) periodic trajectory.
• [00:45 - 00:51] Preset 6/10: Triângulo de Lagrange — Three bodies placed at the vertices of an equilateral triangle rotating in equilibrium before transitioning toward chaotic perturbation.
• [00:52 - 01:06] Preset 7/10: Problema pitagórico de Burrau (3-4-5) — Simulation of Carl Burrau’s classic 1913 Pythagorean problem (masses 3, 4, 5 placed at vertices of a 3:4:5 right triangle at rest), culminating in chaotic mutual close approaches and the high-speed gravitational ejection of the lightest body [01:05].
• [01:07 - 01:24] Preset 8/10: Estrela, planeta e lua — A hierarchical system showing a planet and orbiting satellite tracing epicyclic paths around a massive central primary star.
• [01:25 - 01:38] Preset 9/10: Planeta de duas estrelas — A circumbinary planetary system with an outer planet orbiting a central close binary star pair.
• [01:39 - 02:09] Preset 10/10: Caos: tres massas ao acaso — Unrestricted three-body chaotic scattering from randomized initial conditions, showing sling assists and close-encounter loops.
• [02:10 - 02:14]: The tour completes and loops back to Preset 1 (Figura-8).

Claims & numbers

• The simulation runs at a steady 60 FPS across all configurations.
• Energy conservation drift (dE/E) remains exceptionally low across periodic trajectories (typically between 0 ppm and 3 ppm), indicating high-precision symplectic numerical integration.
• The title claims the application consists of roughly 1,000 lines of Bend2 code with formally proven program laws, synthesized one-shot via AI.

Notable quotes
There is no voiceover or dialogue in the video; notable UI labels include:

• 3 Corpos | 1/10 Figura-8 (Moore, Chenciner-Montgomery) | 60 FPS | dE/E = 0 ppm [00:00]
• 3 Corpos | 7/10 Problema pitagórico de Burrau (3-4-5) [00:52]
• 3 Corpos | 10/10 Caos: tres massas ao acaso [01:39]

Assessment
This is a direct software screen capture demonstration showcasing the output of high-performance physics code and custom 2D canvas rendering. The simulation operates live in real time as evidenced by the smooth particle trail generation, real-time FPS counter, and continuously evolving potential field lines without cuts.

Lyrics & themes
The video contains no lyrics, speech, or vocal track (entirely instrumental/ambient audio accompaniment or silent application audio). The primary themes are classical gravitational dynamics, deterministic chaos, orbital mechanics, and algorithmic precision.

Lore & references

• Moore, Chenciner & Montgomery: References Cristopher Moore's 1993 numerical discovery and Alain Chenciner and Richard Montgomery's 2000 mathematical proof of the stable figure-8 three-body choreography.
• Šuvakov & Dmitrašinović (2013): The Butterfly (Borboleta), Mariposa, Yin-Yang, and Yarn (Novelo) presets reference Milovan Šuvakov and Veljko Dmitrašinović's milestone discovery of dozens of new families of periodic three-body orbits.
• Burrau (1913): Carl Burrau's Pythagorean problem, one of celestial mechanics' most famous benchmark cases of gravitational three-body chaos leading to slingshot ejection.
• Bend2: The massively parallel, high-level functional programming language created by HigherOrderCO, compiled to massively parallel architectures.

Visual style & craft
The visual output is programmatically rendered graphics in a native window, featuring three distinct primary colors (yellow, magenta/pink, and cyan) with glowing point-source halos, persistent fading trajectory ribbons, and subtle concentric gravitational potential contour lines dynamically redrawn according to the instantaneous Newtonian potential field. The visuals are completely code-driven rather than generated by a video diffusion model.

Described by gemini-3.8-flash on 2026-10-04 from the video's audio and frames.