Clifford Attractor
iterated-maps · 37 views
iterated-mapschaotic
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 discrete-map sensitive dependence.
What standard analysis sees
tail heaviness0.36
asymmetry0.66
occupancy0.87
short-range corr0.14
long-range memory0.14
spectral colour0.93
periodicity0.30
complexity0.50
time-irreversibility0.13
volatility clustering0.47
multifractality0.16
dimensionality0.88
nonstationarity0.26
What the atlas adds
discrete-map sensitive dependence+2.6z
deterministic chaos (positive λ_max, sensitive dependence)
names a discrete-map-scoped estimate, NOT chaos in general — continuous-flow chaos (Lorenz, Rössler) reads weak/neutral here despite being genuinely chaotic; spiky arithmetic sources can false-positive on the finite-time estimateAtlas-extreme metrics the standard bank can’t predict for this source
Ordinal Partition:memory_order | +4.0z | bank-miss 1.7σ |
Predictability:entropy_decay_rate | -2.9z | bank-miss 2.4σ |
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 > free_plate_nodal
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 | 3.69 | |
| Henon Map | 4.04 | |
| Logistic r=3.9 (Near-Full Chaos) | 4.07 |
Which Geometries Light Up
Klein Bottle › Klein Bottle:rank_deficit_max | rank 306/306 | 0.0950 |
Ordinal Partition › Ordinal Partition:memory_order | rank 5/306 | 0.7661 |
Predictability › Predictability:entropy_decay_rate | rank 302/306 | -0.1736 |
Symplectic › Symplectic:phase_reflection_symmetry | rank 303/306 | -0.0466 |
S² × ℝ (Thurston) › S² × ℝ (Thurston):bingham_concentration | rank 303/306 | 0.4546 |
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