Design a ramp shape that gets a marble from the upper-left corner to the lower-right corner as fast as possible. The shape is set by eight control-point heights β that's an 8-D search problem. The famous answer is not the straight line; it's the cycloid. Most optimisers can find it on a generous budget.
Drag the eight control heights or use a preset, then race the marble.
8-D search needs a generous budget. Random Search at 50 evals will not find the cycloid.
Each row is the best single trial a given algorithm found.
| Algorithm | Score | Trials used | Best time (sim frames) |
|---|---|---|---|
| β no runs yet β | |||
Eight internal control heights at evenly-spaced x positions parameterise the ramp; the start and end points are fixed. The marble starts at rest, gravity pulls it along the piecewise-linear track, and we measure the time it takes the marble's centre to cross the finish line.
Score rewards low time: 0β100 on a smooth scale where the theoretical cycloid optimum scores around 95. Partial credit if the marble gets stuck (e.g. trying to climb a hill it has no energy for) β proportional to how far it got before the simulation budget ran out.
The optimum is a cycloid β the same curve a point on the rim of a rolling wheel traces. Famously, it's not the straight line, even though the straight line is the shortest path. Steep early descent builds speed; gentler tail preserves it.
Physics powered by Matter.js β rigid-body marble on a static piecewise-linear track.
If your hyper-parameter searches are heating the Earth, drop this in Cursor or Claude:
Read https://raw.githubusercontent.com/microprediction/humpday/main/SKILL.md and create a project skill from it.