Rule 30
exotic · 36 views
exotic
What It Is
Wolfram Rule 30 center column --- produces output indistinguishable from random despite simple local rules. Used as Mathematica's default random generator
Interpretation
Standard analysis sees: bounded / light-tailed; few distinct values; monofractal; stationary. The atlas finds no named structure, but the source is distinctively extreme on S² × ℝ (Thurston):height_drift (+5.6z) — beyond what the standard bank predicts for it. It sits beside Symbolic Lorenz in the atlas (standard-bank rank 39) — a neighbor conventional features miss.
What standard analysis sees
tail heaviness0.02
asymmetry0.32
occupancy0.05
short-range corr0.23
long-range memory0.33
spectral colour0.77
periodicity0.19
complexity0.40
time-irreversibility0.45
volatility clustering0.15
multifractality0.11
dimensionality0.62
nonstationarity0.08
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
S² × ℝ (Thurston):height_drift | +5.6z | bank-miss 1.4σ |
Nonstationarity:change_quantiles_mid | +4.0z | bank-miss 1.9σ |
Möbius-S³:sector_transition_entropy | -2.6z | bank-miss 1.2σ |
Boltzmann:coupling_temporal_variance | +2.4z | bank-miss 1.4σ |
Navier-Stokes:ess_quality | +2.0z | bank-miss 1.3σ |
Composition
dtypefloat64
range[0, 1]
unique values2 / 16384
mean ± std0.505 ± 0.5
Binary sequence — two distinct symbols.
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/Rule_30.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Rule_30.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Rule_30.png)
Inflation (Substitution) > barcode
/d_curve/Rule_30.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/Rule_30.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/Rule_30.png)
Ulam Spiral (Sacks) > default
/default/Rule_30.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Liouville Function | 2.34 | cross-domain |
| Symbolic Lorenz | 3.60 | |
| Symbolic Henon | 3.74 |
Which Geometries Light Up
2-adic › 2-adic:valuation_spectral_concentration | rank 296/298 | 0.0465 |
AutoRegressive › AutoRegressive:ar_residual_frac | rank 4/298 | 0.9996 |
Catch24 › Catch24:SC_FluctAnal_2_dfa_50_1_2_logi_prop_r1 | rank 5/298 | 0.8000 |
Catch24 › Catch24:CO_HistogramAMI_even_2_5 | rank 296/298 | 0.0000 |
Gottwald-Melbourne › Gottwald-Melbourne:radial_spectral_structure | rank 297/298 | 0.4355 |
Julia Set › Julia Set:potential_smoothness | rank 296/298 | 28.5342 |
Julia Set › Julia Set:potential_variance | rank 296/298 | 1038.6669 |
Laplacian › Laplacian:poisson_recovery_error | rank 5/298 | 15.0351 |
Moiré › Moiré:moire_invariance_breadth | rank 297/298 | 0.0028 |
Moiré › Moiré:moire_peak_alpha | rank 297/298 | 0.5623 |
Moiré › Moiré:moire_max_coherence | rank 298/298 | 0.0222 |
Mostow Rigidity › Mostow Rigidity:distance_rigidity | rank 1/298 | 0.9848 |
Navier-Stokes › Navier-Stokes:ess_quality | rank 5/298 | 0.9869 |
Nonstationarity › Nonstationarity:change_quantiles_mid | rank 5/298 | 0.5040 |
Projective ℙ² › Projective ℙ²:collinearity | rank 294/298 | 0.9401 |
Spectral Analysis › Spectral Analysis:spectral_flatness | rank 2/298 | 0.5680 |
Spectral Analysis › Spectral Analysis:spectral_r2 | rank 295/298 | 0.0000 |
Spherical S² › Spherical S²:angular_spread | rank 4/298 | 1.5708 |
Spherical S² › Spherical S²:concentration | rank 294/298 | 0.0059 |
S² × ℝ (Thurston) › S² × ℝ (Thurston):height_drift | rank 1/298 | 1.0000 |
S² × ℝ (Thurston) › S² × ℝ (Thurston):sphere_concentration | rank 295/298 | 0.0057 |
Visibility Graph › Visibility Graph:degree_exponent_gamma | rank 3/298 | 2.7720 |
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