Magnetic Pendulum (3-Magnet)
continuous-flows · 37 views
continuous-flowschaotic
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 additionally detects Multifractal Spectrum:hurst_estimate. It sits beside Chua's Circuit in the atlas (standard-bank rank 26) — a neighbor conventional features miss.
What standard analysis sees
tail heaviness0.44
asymmetry0.60
occupancy0.85
short-range corr0.98
long-range memory0.98
spectral colour0.18
periodicity0.77
complexity0.04
time-irreversibility0.76
volatility clustering0.99
multifractality0.92
dimensionality0.18
nonstationarity0.76
What the atlas adds
Multifractal Spectrum:hurst_estimate+2.9z
self-affinity H = τ(2)/2 (alternate to Hölder hurst)
Atlas-extreme metrics the standard bank can’t predict for this source
Moiré:moire_invariance_breadth | +3.0z | bank-miss 1.4σ |
Ammann-Beenker (Octagonal):convergent_resonance | +2.3z | bank-miss 1.3σ |
Composition
dtypefloat64
range[-1.798, 1.937]
unique values16222 / 16384
mean ± std-0.0067 ± 1.08
Render Gallery
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Native > phase_plotraw
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Native > timeseriesraw
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Native > triple_latticeraw
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Boltzmann > lag_map
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Boltzmann > spin_grid
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Cayley > default
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Chladni > free_plate_nodal
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Chladni > plate_bottom
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Chladni > plate_top
_(centered)/signed_log_z/Magnetic_Pendulum_(3-Magnet).png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Magnetic_Pendulum_(3-Magnet).png)
Heisenberg (Nil) (centered) > xy_path
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Hodge–Laplacian > default
/barcode/Magnetic_Pendulum_(3-Magnet).png)
Inflation (Substitution) > barcode
/d_curve/Magnetic_Pendulum_(3-Magnet).png)
Inflation (Substitution) > d_curve
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Information Theory > default
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Julia Set > escape_histogram
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Klein Bottle > default
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Laplacian > default
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Logarithmic Spiral > default
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Möbius-S³ > mobius_cylinder
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Möbius-S³ > s2_base_map
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Ordinal Partition > default
/phi_spectrum/Magnetic_Pendulum_(3-Magnet).png)
Penrose (Quasicrystal) > phi_spectrum
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Persistent Homology > barcode
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Persistent Homology > h1_diagram
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Predictability > default
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Recurrence Quantification > default
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Spectral Analysis > default
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Spectral Graph > default
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Spirograph > mode_spectrum
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Spirograph > phasor_trajectory
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Symplectic > flux_grid
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Symplectic > phase_space
/default/Magnetic_Pendulum_(3-Magnet).png)
Ulam Spiral (Sacks) > default
/default/Magnetic_Pendulum_(3-Magnet).png)
Ulam Spiral (Square) > default
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Visibility Graph > default
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Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Chua's Circuit | 2.70 | |
| Spring Pendulum | 2.88 | |
| Duffing Oscillator | 2.92 |
Which Geometries Light Up
Ammann-Beenker (Octagonal) › Ammann-Beenker (Octagonal):convergent_resonance | rank 4/307 | 0.9000 |
Bispectrum › Bispectrum:coupling_frequency_centroid | rank 5/307 | 0.6192 |
Catch24 › Catch24:CO_Embed2_Dist_tau_d_expfit_meandiff | rank 2/307 | 56.9308 |
Catch24 › Catch24:SB_BinaryStats_diff_longstretch0 | rank 5/307 | 775.2000 |
Catch24 › Catch24:FC_LocalSimple_mean3_stderr | rank 303/307 | 0.0110 |
Chladni › Chladni:captured_power_fraction | rank 305/307 | 0.0006 |
Hodge–Laplacian › Hodge–Laplacian:curl_div_ratio | rank 3/307 | 5.8527 |
Hodge–Laplacian › Hodge–Laplacian:solenoidal_fraction | rank 4/307 | 0.9967 |
H² × ℝ (Thurston) › H² × ℝ (Thurston):hyperbolic_triangle_area | rank 304/307 | 0.0001 |
Hölder Regularity › Hölder Regularity:holder_min | rank 5/307 | 0.9227 |
Laplacian › Laplacian:gradient_sign_persistence | rank 2/307 | 0.9976 |
Moiré › Moiré:moire_invariance_breadth | rank 2/307 | 0.0380 |
Möbius-S³ › Möbius-S³:hopf_fiber_coherence | rank 3/307 | 0.8039 |
Projective ℙ² › Projective ℙ²:distance_std | rank 303/307 | 0.0001 |
Spectral Analysis › Spectral Analysis:spectral_r2 | rank 4/307 | 0.9658 |
Symplectic › Symplectic:flux_sign_persistence | rank 5/307 | 277.9894 |
Ulam Spiral (Square) › Ulam Spiral (Square):radon_anisotropy | rank 2/307 | 0.0421 |
Visibility Graph › Visibility Graph:nvg_hvg_reach_divergence | rank 2/307 | 0.9974 |
p-Variation › p-Variation:volatility_clustering | rank 1/307 | 0.9998 |
p-Variation › p-Variation:variation_index | rank 304/307 | 1.0005 |
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