Tank Drain Cascade
exotic · 36 views
exotic
What It Is
Filling tank with multiplicative partial drains: x grows at constant rate to saturation K, at Poisson rate drains to x*Uniform(0, 0.5). Random drain magnitude mirrors Forest Fire's variable fire-cluster sizes. Positive control for slow-build + sudden-drop phenotype with non-uniform drop magnitudes
Interpretation
Standard analysis sees: left-skewed; long-range memory (persistent); low-complexity (predictable, not noise-like); time-irreversible (slow rise, sharp collapse); low-dimensional. The atlas finds no named structure, but the source is distinctively extreme on S² × ℝ (Thurston):height_drift (+4.0z) — beyond what the standard bank predicts for it. It sits beside Stochastic Resetting Walk in the atlas (standard-bank rank 41) — a neighbor conventional features miss.
What standard analysis sees
tail heaviness0.46
asymmetry0.06
occupancy0.79
short-range corr0.75
long-range memory0.89
spectral colour0.27
periodicity0.60
complexity0.01
time-irreversibility0.01
volatility clustering0.80
multifractality0.82
dimensionality0.07
nonstationarity0.69
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
S² × ℝ (Thurston):height_drift | +4.0z | bank-miss 1.2σ |
Wavelet Cascade:intermittency_slope | -3.7z | bank-miss 1.7σ |
WaveformAsymmetry:waveform_asymmetry | +3.4z | bank-miss 1.6σ |
Nonstationarity:vol_of_vol | +3.2z | bank-miss 1.5σ |
Higher-Order Statistics:kurt_max | +3.2z | bank-miss 1.6σ |
SL(2,ℝ) (Thurston):lyapunov_std | +3.2z | bank-miss 1.1σ |
Multifractal Spectrum:spectrum_width | +3.0z | bank-miss 1.2σ |
H² × ℝ (Thurston):depth_height_corr | +2.9z | bank-miss 1.3σ |
Composition
dtypefloat64
range[1.539e-05, 0.9982]
unique values16384 / 16384
mean ± std0.729 ± 0.255
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/Tank_Drain_Cascade.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Tank_Drain_Cascade.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Tank_Drain_Cascade.png)
Inflation (Substitution) > barcode
/d_curve/Tank_Drain_Cascade.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/Tank_Drain_Cascade.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/Tank_Drain_Cascade.png)
Ulam Spiral (Sacks) > default
/default/Tank_Drain_Cascade.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Sawtooth Wave | 4.57 | cross-domain |
| Stochastic Resetting Walk | 4.83 | |
| Pressure | 4.90 | cross-domain |
Which Geometries Light Up
Catch24 › Catch24:DN_Mean | rank 5/298 | 0.7229 |
D4 Triality › D4 Triality:edge_ortho_polarity | rank 4/298 | 0.7398 |
Higher-Order Statistics › Higher-Order Statistics:kurt_max | rank 5/298 | 6.3934 |
Higher-Order Statistics › Higher-Order Statistics:perm_entropy | rank 295/298 | 0.0141 |
H² × ℝ (Thurston) › H² × ℝ (Thurston):depth_height_corr | rank 2/298 | 0.6782 |
H² × ℝ (Thurston) › H² × ℝ (Thurston):hyperbolic_variance | rank 4/298 | 3.3145 |
Hölder Regularity › Hölder Regularity:holder_min | rank 3/298 | 0.9964 |
Julia Set › Julia Set:potential_smoothness | rank 298/298 | 10.8135 |
Julia Set › Julia Set:potential_variance | rank 298/298 | 117.6809 |
Laplacian › Laplacian:laplacian_evolutionary_index | rank 5/298 | 0.4621 |
Navier-Stokes › Navier-Stokes:cascade_asymmetry | rank 297/298 | -0.9998 |
Piecewise-Linear › Piecewise-Linear:envelope_area | rank 3/298 | 11697.5263 |
SL(2,ℝ) (Thurston) › SL(2,ℝ) (Thurston):lyapunov_std | rank 4/298 | 0.6442 |
S² × ℝ (Thurston) › S² × ℝ (Thurston):height_drift | rank 4/298 | 0.7191 |
Time Reversibility › Time Reversibility:increment_skewness_max | rank 3/298 | 1.0000 |
WaveformAsymmetry › WaveformAsymmetry:waveform_asymmetry | rank 2/298 | 0.9946 |
Wavelet Cascade › Wavelet Cascade:intermittency_slope | rank 295/298 | -2.6218 |
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