Random Steps
stochastic-process · 37 views
stochastic-processstochastic
What It Is
Random piecewise-constant signal --- flat plateaus of random height with geometrically-distributed durations, creating a sparse derivative and blocky texture
Interpretation
Standard analysis sees: low-complexity (predictable, not noise-like); time-irreversible (slow rise, sharp collapse); multifractal. The atlas finds no named structure, but the source is distinctively extreme on D4 Triality:edge_ortho_polarity (-4.8z) — beyond what the standard bank predicts for it. It sits beside ECG Ventricular in the atlas (standard-bank rank 58) — a neighbor conventional features miss.
What standard analysis sees
tail heaviness0.18
asymmetry0.19
occupancy0.51
short-range corr0.73
long-range memory0.82
spectral colour0.32
periodicity0.50
complexity0.02
time-irreversibility0.15
volatility clustering0.76
multifractality0.99
dimensionality0.31
nonstationarity0.66
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
D4 Triality:edge_ortho_polarity | -4.8z | bank-miss 2.1σ |
Fisher Information:geodesic_velocity | +3.6z | bank-miss 1.9σ |
E8 Lattice:coset_transition | +2.9z | bank-miss 1.2σ |
Mostow Rigidity:volume_entropy | -2.9z | bank-miss 1.3σ |
Laplacian:poisson_recovery_error | -2.5z | bank-miss 1.1σ |
Projective ℙ²:cross_ratio_std | -2.4z | bank-miss 2.2σ |
Chladni:domain_ks_exponential | -2.4z | bank-miss 1.7σ |
G2 Root System:pair_angle_kurtosis | +2.3z | bank-miss 1.1σ |
Composition
dtypeuint8
range[1, 255]
unique values171 / 16384
mean ± std136 ± 76.9
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
_(centered)/signed_log_z/Random_Steps.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Random_Steps.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Random_Steps.png)
Inflation (Substitution) > barcode
/d_curve/Random_Steps.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/Random_Steps.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/Random_Steps.png)
Ulam Spiral (Sacks) > default
/default/Random_Steps.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Triple Pendulum | 4.75 | cross-origin |
| ECG Ventricular | 4.84 | cross-origin |
| Lorenz-96 N=8 | 4.91 | cross-origin |
Which Geometries Light Up
Chladni › Chladni:domain_ks_exponential | rank 304/306 | 0.0559 |
D4 Triality › D4 Triality:edge_ortho_polarity | rank 302/306 | 0.0351 |
E8 Lattice › E8 Lattice:coset_transition | rank 5/306 | 0.1848 |
Fisher Information › Fisher Information:geodesic_velocity | rank 1/306 | 1.8645 |
G2 Root System › G2 Root System:pair_angle_kurtosis | rank 5/306 | 67.8763 |
G2 Root System › G2 Root System:short_long_ratio | rank 5/306 | 0.9902 |
Laplacian › Laplacian:poisson_recovery_error | rank 303/306 | 0.0052 |
Multi-Scale Wasserstein › Multi-Scale Wasserstein:w_mean | rank 5/306 | 0.1334 |
Predictability › Predictability:excess_predictability | rank 5/306 | 2.8121 |
Projective ℙ² › Projective ℙ²:cross_ratio_std | rank 302/306 | 0.0103 |
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