Rule 30
symbolic-dynamics · 37 views
symbolic-dynamicssymbolic
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 38) — a neighbor conventional features miss.
What standard analysis sees
tail heaviness0.02
asymmetry0.32
occupancy0.05
short-range corr0.23
long-range memory0.32
spectral colour0.77
periodicity0.19
complexity0.40
time-irreversibility0.45
volatility clustering0.16
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 | +5.5z | bank-miss 1.4σ |
Nonstationarity:change_quantiles_mid | +4.0z | bank-miss 1.6σ |
Spherical S²:angular_spread | +3.4z | bank-miss 1.0σ |
Möbius-S³:sector_transition_entropy | -2.7z | bank-miss 1.1σ |
Modular Residue:occupancy_entropy | -2.4z | bank-miss 1.3σ |
Boltzmann:coupling_temporal_variance | +2.4z | bank-miss 1.8σ |
Navier-Stokes:ess_quality | +2.0z | bank-miss 1.2σ |
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 > free_plate_nodal
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 | 2.32 | cross-origin |
| Symbolic Lorenz | 3.46 | cross-origin |
| Symbolic Henon | 3.49 | cross-origin |
Which Geometries Light Up
2-adic › 2-adic:valuation_spectral_concentration | rank 305/307 | 0.0465 |
AutoRegressive › AutoRegressive:ar_residual_frac | rank 4/307 | 0.9996 |
Catch24 › Catch24:SC_FluctAnal_2_dfa_50_1_2_logi_prop_r1 | rank 4/307 | 0.8000 |
Catch24 › Catch24:CO_HistogramAMI_even_2_5 | rank 305/307 | 0.0000 |
G2 Root System › G2 Root System:pair_angle_kurtosis | rank 305/307 | -1.9987 |
Julia Set › Julia Set:potential_smoothness | rank 304/307 | 28.5342 |
Julia Set › Julia Set:potential_variance | rank 305/307 | 1038.6669 |
Moiré › Moiré:moire_invariance_breadth | rank 306/307 | 0.0028 |
Moiré › Moiré:moire_max_coherence | rank 306/307 | 0.0222 |
Moiré › Moiré:moire_peak_alpha | rank 306/307 | 0.5623 |
Mostow Rigidity › Mostow Rigidity:distance_rigidity | rank 1/307 | 0.9848 |
Navier-Stokes › Navier-Stokes:ess_rescaling_gain | rank 5/307 | 0.9869 |
Spectral Analysis › Spectral Analysis:spectral_r2 | rank 304/307 | 0.0000 |
Spherical S² › Spherical S²:angular_spread | rank 4/307 | 1.5708 |
Spherical S² › Spherical S²:concentration | rank 303/307 | 0.0059 |
S² × ℝ (Thurston) › S² × ℝ (Thurston):height_drift | rank 1/307 | 1.0000 |
S² × ℝ (Thurston) › S² × ℝ (Thurston):sphere_concentration | rank 304/307 | 0.0057 |
Visibility Graph › Visibility Graph:degree_exponent_gamma | rank 3/307 | 2.7720 |
← / → within domain · ⇧← / ⇧→ alphabetical · ⇧← / ⇧→ inside an open render = same view across sources