Magnetic Pendulum (3-Magnet)

What It Is

Pendulum tip in 2D plane above three magnets at triangle vertices, with linear gravity-restoring force --- conservative (no damping) 2-DOF Hamiltonian chaos. The damped version has the famous fractal basin boundaries; the undamped version sweeps the energy surface chaotically. Velocity-Verlet (symplectic) integration. Output: x(t).

Interpretation

Standard analysis sees: rich, high-entropy values; smooth / autocorrelated; long-range memory (persistent); low-complexity (predictable, not noise-like); volatility-clustering (bursty); multifractal. The atlas finds no named structure, but the source is distinctively extreme on Moiré:moire_invariance_breadth (+3.1z) — beyond what the standard bank predicts for it. It sits beside Hénon-Heiles in the atlas (standard-bank rank 29) — a neighbor conventional features miss.

Composition

Render Gallery

Native > phase_plotraw

Native > timeseriesraw

Native > triple_latticeraw

Boltzmann > lag_map

Boltzmann > spin_grid

Cayley > default

Chladni > plate_bottom

Chladni > plate_top

Heisenberg (Nil) (centered) > signed_log_z

Heisenberg (Nil) (centered) > xy_path

Hodge–Laplacian > default

Inflation (Substitution) > barcode

Inflation (Substitution) > d_curve

Information Theory > default

Julia Set > escape_histogram

Klein Bottle > default

Laplacian > default

Logarithmic Spiral > default

Möbius-S³ > mobius_cylinder

Möbius-S³ > s2_base_map

Ordinal Partition > default

Penrose (Quasicrystal) > phi_spectrum

Persistent Homology > barcode

Persistent Homology > h1_diagram

Predictability > default

Recurrence Quantification > default

Spectral Analysis > default

Spectral Graph > default

Spirograph > mode_spectrum

Spirograph > phasor_trajectory

Symplectic > flux_grid

Symplectic > phase_space

Ulam Spiral (Sacks) > default

Ulam Spiral (Square) > default

Visibility Graph > default

Wavelet Cascade > default

Atlas Position

Open in Atlas →

Which Geometries Light Up