Markov Chain (10-state)
stochastic-process · 37 views
stochastic-processstochastic
What It Is
Ergodic 10-state Markov chain. Moderate entropy, smooth spectrum, diverse transitions.
Interpretation
Standard analysis sees: bounded / light-tailed; aperiodic / broadband; stationary. The atlas finds no named structure, but the source is distinctively extreme on Nonstationarity:change_quantiles_low (+2.1z) — beyond what the standard bank predicts for it. It sits beside Categorical Sensor in the atlas (standard-bank rank 21) — a neighbor conventional features miss.
What standard analysis sees
tail heaviness0.06
asymmetry0.65
occupancy0.18
short-range corr0.44
long-range memory0.40
spectral colour0.57
periodicity0.15
complexity0.62
time-irreversibility0.15
volatility clustering0.40
multifractality0.26
dimensionality0.69
nonstationarity0.15
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
Nonstationarity:change_quantiles_low | +2.1z | bank-miss 3.3σ |
Composition
dtypeuint8
range[6, 200]
unique values10 / 16384
mean ± std108 ± 64.4
Fixed alphabet — only 10 distinct symbols across 16384 samples.
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/Markov_Chain_(10-state).png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Markov_Chain_(10-state).png)
Heisenberg (Nil) (centered) > xy_path
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Hodge–Laplacian > default
/barcode/Markov_Chain_(10-state).png)
Inflation (Substitution) > barcode
/d_curve/Markov_Chain_(10-state).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/Markov_Chain_(10-state).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/Markov_Chain_(10-state).png)
Ulam Spiral (Sacks) > default
/default/Markov_Chain_(10-state).png)
Ulam Spiral (Square) > default
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Visibility Graph > default
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Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Dice Rolls | 3.42 | |
| Categorical Sensor | 3.51 | |
| Codon Usage | 3.79 | cross-origin |
Which Geometries Light Up
This source does not rank extreme on any metric.
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