Clifford Attractor
chaos · 36 views
chaos
What It Is
Clifford 2D iterated map x_{n+1}=sin(a*y)+c*cos(a*x), y_{n+1}=sin(b*x)+d*cos(b*y) at (a,b,c,d)=(-1.4,1.6,1.0,0.7). Bounded sin/cos-coupled discrete chaos with rich fractal fine structure, distinct from Hénon's quadratic folding. Output: x-coordinate.
Interpretation
Standard analysis sees: rich, high-entropy values; anti-correlated (alternating); anti-persistent; blue spectrum (high-frequency power); time-irreversible (slow rise, sharp collapse); high-dimensional / space-filling. The atlas additionally detects deterministic chaos, combinatorially flat (normal-sequence).
What standard analysis sees
tail heaviness0.36
asymmetry0.69
occupancy0.87
short-range corr0.14
long-range memory0.14
spectral colour0.93
periodicity0.30
complexity0.48
time-irreversibility0.13
volatility clustering0.45
multifractality0.27
dimensionality0.97
nonstationarity0.32
What the atlas adds
deterministic chaos+3.1z
positive largest Lyapunov exponent — nearby trajectories diverge exponentially (sensitive dependence)
discrete-map biased — continuous-flow chaos (Lorenz) reads weak; spiky arithmetic sources can false-positive on the finite-time estimatecombinatorially flat (normal-sequence)+2.8z
every fixed-length block is near-equiprobable and longer context yields no extra predictability — the De Bruijn / normal-number signature (distinct from random noise, which sits mid-scale)
names deterministic flatness — IID noise sits neutral, NOT at this poleAtlas-extreme metrics the standard bank can’t predict for this source
Ordinal Partition:memory_order | +3.8z | bank-miss 1.0σ |
Composition
dtypefloat64
range[-1.414, 1.979]
unique values16384 / 16384
mean ± std0.202 ± 0.906
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/Clifford_Attractor.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Clifford_Attractor.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Clifford_Attractor.png)
Inflation (Substitution) > barcode
/d_curve/Clifford_Attractor.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/Clifford_Attractor.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/Clifford_Attractor.png)
Ulam Spiral (Sacks) > default
/default/Clifford_Attractor.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Ikeda Map | 3.88 | |
| Henon Map | 4.17 | |
| Logistic r=3.9 (Near-Full Chaos) | 4.27 |
Which Geometries Light Up
Hölder Regularity › Hölder Regularity:holder_std | rank 5/298 | 1.8042 |
Klein Bottle › Klein Bottle:rank_deficit_max | rank 297/298 | 0.1014 |
Ordinal Partition › Ordinal Partition:memory_order | rank 5/298 | 0.7643 |
Predictability › Predictability:entropy_decay_rate | rank 294/298 | -0.1730 |
Symplectic › Symplectic:phase_reflection_symmetry | rank 295/298 | -0.0456 |
S² × ℝ (Thurston) › S² × ℝ (Thurston):bingham_concentration | rank 295/298 | 0.4546 |
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