Triple Pendulum

What It Is

3-segment Lagrangian pendulum chain, equal m=L=1 --- Hamiltonian 3-DOF conservative chaos with sin-coupling. Direct extension of Double Pendulum by one link; meant to populate the multi-DOF pendulum family the way Lorenz-96 {N=4,8,36} populates the dissipative-chain family. RK4 with dt=0.002. Output: angular velocity of bottom segment.

Interpretation

Standard analysis sees: smooth / autocorrelated; long-range memory (persistent); red spectrum (low-frequency / 1-over-f power); low-complexity (predictable, not noise-like); volatility-clustering (bursty); multifractal. The atlas additionally detects Multifractal Spectrum:hurst_estimate.

Composition

Render Gallery

Native > phase_plotraw

Native > timeseriesraw

Native > triple_latticeraw

Boltzmann > lag_map

Boltzmann > spin_grid

Cayley > default

Chladni > free_plate_nodal

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