Packing lab: Monte Carlo sandbox nudges within 0.04% of published 5D sphere packing
idanbeck · x · 2026-10-12
A fun interactive geometric sandbox for high-dimensional packing: particles start soft, get compressed and annealed into hard cubes via a Monte Carlo loop running in a background worker, with live 4D/5D projections into 3D.
- The 5D experiment (40 cubes, 6,000 iterations) reaches a container side of 2.9172, only 0.0429% larger than the published (not necessarily optimal) packing
- The 4D run (17 tesseracts) yields a side of 2.6604 with all 17 center distances above 0.87 and 22% center-distance variance
- The UI ships live measurements, scrubbable run trajectories and projection checks to verify feasibility and gaps
Beyond the math, it's a nice example of turning a numerical experiment into an explorable, measurable sandbox.
More from Research
- SoftwareGym synthesizes 182 app environments, lifting CUA OSWorld Pass@3 to 56.97% — Tian Jin · 2026-10-12
- Qualcomm AI uses entropy and CKA to pick layers, beating EAGLE3 defaults in speculative decoding — Qualcomm-AI-Research · 2026-10-12
- Evolved e-puck robots show communication emerges with information value — uv-mex · 2026-10-12
- PreSTO Speeds Up LLM Power Sampling Up to 2.33x via Predictive Subtree Prefetching — du_yilun · 2026-10-12
- AWS+HSBC paper co-evolves agent graders from just 10 labeled examples, matching ground truth — rohanpaul_ai · 2026-10-12
- Nature MI paper: LLMs discover complementary heuristics for combinatorial optimization — lulzxdxdxd · 2026-10-12