Gray Code Counter
symbolic-dynamics · 37 views
symbolic-dynamicssymbolic
What It Is
8-bit Gray-code counter with variable step. Low entropy, high structure, complex bit transitions.
Interpretation
Standard analysis sees: rich, high-entropy values; strongly periodic; stationary. The atlas finds no named structure, but the source is distinctively extreme on Penrose (Quasicrystal):phi_tower (-9.2z) — beyond what the standard bank predicts for it. It sits beside De Bruijn Sequence in the atlas (standard-bank rank 61) — a neighbor conventional features miss.
What standard analysis sees
tail heaviness0.24
asymmetry0.41
occupancy0.99
short-range corr0.70
long-range memory0.56
spectral colour0.28
periodicity0.90
complexity0.57
time-irreversibility0.48
volatility clustering0.69
multifractality0.53
dimensionality0.19
nonstationarity0.00
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
Penrose (Quasicrystal):phi_tower | -9.2z | bank-miss 4.0σ |
Multi-Scale Wasserstein:w_slope | +8.1z | bank-miss 2.4σ |
Gottwald-Melbourne:k_variance | +4.8z | bank-miss 1.0σ |
Fisher Information:velocity_spectral_gini | -4.2z | bank-miss 2.0σ |
Klein Bottle:wht_spectral_kurtosis | +3.5z | bank-miss 2.1σ |
Chladni:nodal_gap_ratio | +2.3z | bank-miss 3.3σ |
Higher-Order Statistics:bicoherence_max | +2.2z | bank-miss 2.4σ |
E8 Lattice:coset_transition | +2.1z | bank-miss 1.5σ |
Composition
dtypeuint8
range[0, 254]
unique values128 / 16384
mean ± std127 ± 73.9
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/Gray_Code_Counter.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Gray_Code_Counter.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Gray_Code_Counter.png)
Inflation (Substitution) > barcode
/d_curve/Gray_Code_Counter.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/Gray_Code_Counter.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/Gray_Code_Counter.png)
Ulam Spiral (Sacks) > default
/default/Gray_Code_Counter.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Triangle Wave | 5.04 | cross-origin |
| De Bruijn Sequence | 5.16 | |
| Clipped Sine | 5.17 | cross-origin |
Which Geometries Light Up
Ammann-Beenker (Octagonal) › Ammann-Beenker (Octagonal):convergent_profile | rank 303/307 | -0.1462 |
Fisher Information › Fisher Information:effective_dimension | rank 2/307 | 16.0000 |
Fisher Information › Fisher Information:log_det_fisher | rank 306/307 | 44.3614 |
Fisher Information › Fisher Information:trace_fisher | rank 307/307 | 256.0000 |
Gottwald-Melbourne › Gottwald-Melbourne:k_variance | rank 3/307 | 0.7746 |
Klein Bottle › Klein Bottle:wht_spectral_kurtosis | rank 4/307 | 8.8286 |
Multi-Scale Wasserstein › Multi-Scale Wasserstein:w_slope | rank 2/307 | 6.3514 |
Penrose (Quasicrystal) › Penrose (Quasicrystal):phi_tower | rank 307/307 | -7.1242 |
Spherical S² › Spherical S²:hemisphere_balance | rank 1/307 | 1.0000 |
Wasserstein › Wasserstein:entropy | rank 1/307 | 5.0000 |
Wasserstein › Wasserstein:concentration | rank 307/307 | 1.0000 |
Wasserstein › Wasserstein:dist_from_uniform | rank 307/307 | 0.0000 |
Zipf–Mandelbrot (16-bit) › Zipf–Mandelbrot (16-bit):gini_coefficient | rank 303/307 | 0.0001 |
Zipf–Mandelbrot (8-bit) › Zipf–Mandelbrot (8-bit):zipf_r_squared | rank 2/307 | 1.0000 |
Zipf–Mandelbrot (8-bit) › Zipf–Mandelbrot (8-bit):gini_coefficient | rank 307/307 | 0.0000 |
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