Top-down view of a pendulum bob pulled by gravity toward the pivot's ground point and sideways by fixed magnets. The shaded background is a computed
map: the color under any point shows which magnet a bob released there — at rest — would ultimately be captured by.
Each pixel of the basin map is its own independent physics simulation: a bob is placed at rest at that point and integrated forward until it settles near a magnet (or a step limit is hit), and the pixel is colored by the winning magnet, darkened by how many steps it took to get there. Basins are computed progressively in the background — the picture sharpens over a few seconds. Neighboring pixels can settle on completely different magnets: that fine, fractal-like interleaving of colors is chaos made visible without any animation running.
- The live bob (white dot) follows the exact same equations used to build the map, so its trail should end on the color it currently sits over.
- Basin boundaries are fractal — increase magnet count or strength and recompute to see the interleaving grow finer.
- Damping models air drag and eddy-current braking; raise it and captures happen faster with a smoother map.
- Because the system is deterministic, identical start points always settle on the same magnet, every run.
- Recompute the map after changing magnet count or strength — old maps go stale instantly.