PID Controller
exotic · 36 views
exotic
What It Is
PID controller tracking a step-changing setpoint. Deterministic, narrowband, strongly correlated.
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; low-dimensional; nonstationary / drifting. The atlas finds no named structure, but the source is distinctively extreme on Persistent Homology:persistence_entropy (-3.7z) — beyond what the standard bank predicts for it.
What standard analysis sees
tail heaviness0.38
asymmetry0.23
occupancy0.67
short-range corr0.98
long-range memory0.99
spectral colour0.11
periodicity0.76
complexity0.06
time-irreversibility0.85
volatility clustering0.98
multifractality0.95
dimensionality0.13
nonstationarity0.89
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
Persistent Homology:persistence_entropy | -3.7z | bank-miss 1.4σ |
Persistent Homology:total_persistence | -2.6z | bank-miss 1.3σ |
Fisher Information:geodesic_velocity | +2.6z | bank-miss 1.6σ |
Composition
dtypefloat64
range[-1.794, 1.535]
unique values16121 / 16384
mean ± std0.101 ± 0.831
Render Gallery
Native > phase_plotraw
Native > timeseriesraw
Native > triple_latticeraw
Boltzmann > lag_map
Boltzmann > spin_grid
Cayley > default
Chladni > plate_bottom
Chladni > plate_top
_(centered)/signed_log_z/PID_Controller.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/PID_Controller.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/PID_Controller.png)
Inflation (Substitution) > barcode
/d_curve/PID_Controller.png)
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
/phi_spectrum/PID_Controller.png)
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
/default/PID_Controller.png)
Ulam Spiral (Sacks) > default
/default/PID_Controller.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Triple Pendulum | 3.37 | cross-domain |
| FPUT N=16 | 3.73 | cross-domain |
| Magnetic Pendulum (3-Magnet) | 4.07 | cross-domain |
Which Geometries Light Up
AutoRegressive › AutoRegressive:ar_residual_frac | rank 295/298 | 0.0000 |
Catch24 › Catch24:PD_PeriodicityWang_th0_01 | rank 2/298 | 3564.1000 |
Catch24 › Catch24:SB_BinaryStats_diff_longstretch0 | rank 4/298 | 1160.2000 |
Fractal (Mandelbrot) › Fractal (Mandelbrot):potential_roughness | rank 294/298 | 0.0079 |
Gottwald-Melbourne › Gottwald-Melbourne:angular_spectral_structure | rank 3/298 | 0.9899 |
H² × ℝ (Thurston) › H² × ℝ (Thurston):hyperbolic_step_dispersion | rank 294/298 | 0.0320 |
Persistent Homology › Persistent Homology:total_persistence | rank 294/298 | 1.1717 |
Persistent Homology › Persistent Homology:persistence_entropy | rank 296/298 | 0.2738 |
Visibility Graph › Visibility Graph:nvg_hvg_reach_divergence | rank 5/298 | 0.9949 |
Wasserstein › Wasserstein:recurrence_distance | rank 1/298 | 0.1077 |
Wavelet Cascade › Wavelet Cascade:cascade_coupling | rank 4/298 | 0.8124 |
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