damiavicens/magnetic-pendulum-films

The magnetic pendulum in 2D — basin-of-attraction films

Four 1080p60 films, ~30 s each, of the basin-of-attraction map of the magnetic pendulum: release the bob from rest at every point of the plane, integrate until it settles, and colour that point by the magnet that captured it.

This is a real, named, well-studied object, not a repurposed Newton fractal. Its signature is the Wada property: every point on the boundary between two basins is also on the boundary of the third, at any magnification.

The model

r'' = -k_g r - k_f v + sum_i k_i (p_i - r) / (|p_i - r|^2 + h_i^2)^((q+1)/2)

with h the bob's height above the magnet plane, which softens the singularity. Defaults k_g = 1, k_f = 0.20, h = 0.25, q = 2 (the canonical inverse-square toy model), three magnets at unit radius.

The films

film	what
A	the picture builds itself: one real launch at real speed, then a time lapse filling the canvas in Halton order, then the finished map
B	the atlas: magnet separation, unequal strengths, count N = 2 to 8 (continuous), damping, force falloff q = 2 to 4, irregular configurations
C	rotating magnets: N = 3 and N = 6 quasi-static, alternating strengths breaking six-fold symmetry to three-fold, counter-rotating rings
D	the same fields shaded as real surfaces: liquid metal, water with moving ripples, thin-film iridescence, glass, lacquer

Method notes

Batched RK4, one CUDA thread per trajectory, with a per-thread early-exit mask (measured 86.9% early exit; mean 10,469 of a possible 80,000 steps). Capture requires the bob to stay inside 0.25 d_min of a magnet and below |v| = 0.02 continuously for 1.5 s — a single-instant test misfires on fast fly-bys and gives a visibly wrong map.

The card is an RTX PRO 6000 Blackwell, whose measured FP64:FP32 ratio is 1:38.2, so the morphs run in f32. That choice was measured, not assumed: the f32-vs-f64 basin label disagreement is 0.004%, far below the 1% threshold.

Colour is a banded Oklch construction — one lightness band per basin at a single hue, gamut-mapped by reducing chroma at fixed L and h — baked to a LUT. Doing the gamut mapping per pixel cost 5.78 s/frame; the LUT does it in 0.235 s.