Dice Rolls
stochastic-process · 37 views
stochastic-processhigh-entropy
What It Is
Simulated dice rolls --- uniform over just 6 levels (0, 51, 102, 153, 204, 255), creating a maximally discrete distribution with IID independence
Interpretation
Standard analysis sees: aperiodic / broadband; high-dimensional / space-filling. The atlas finds no named structure, but the source is distinctively extreme on Zariski:algebraic_residual (+2.7z) — beyond what the standard bank predicts for it. It sits beside Free Group F₂ Walk in the atlas (standard-bank rank 20) — a neighbor conventional features miss.
What standard analysis sees
tail heaviness0.18
asymmetry0.52
occupancy0.16
short-range corr0.32
long-range memory0.22
spectral colour0.68
periodicity0.11
complexity0.75
time-irreversibility0.33
volatility clustering0.24
multifractality0.27
dimensionality0.99
nonstationarity0.18
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
Zariski:algebraic_residual | +2.7z | bank-miss 1.4σ |
Nonstationarity:change_quantiles_low | +2.6z | bank-miss 2.6σ |
Composition
dtypeuint8
range[0, 255]
unique values6 / 16384
mean ± std127 ± 87.2
Fixed alphabet — only 6 distinct symbols across 16384 samples.
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/Dice_Rolls.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Dice_Rolls.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Dice_Rolls.png)
Inflation (Substitution) > barcode
/d_curve/Dice_Rolls.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/Dice_Rolls.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/Dice_Rolls.png)
Ulam Spiral (Sacks) > default
/default/Dice_Rolls.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Markov Chain (10-state) | 3.42 | |
| Euler-Mascheroni γ Digits | 3.87 | cross-origin |
| Free Group F₂ Walk | 3.90 | cross-origin |
Which Geometries Light Up
Attractor Reconstruction › Attractor Reconstruction:filling_ratio | rank 1/307 | 0.9938 |
Mostow Rigidity › Mostow Rigidity:volume_entropy | rank 3/307 | 4.5058 |
Symplectic › Symplectic:recurrence_rate | rank 307/307 | 0.0270 |
Zariski › Zariski:residual_slope | rank 3/307 | -0.6995 |
Zariski › Zariski:algebraic_residual | rank 5/307 | 0.0640 |
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