Logistic r=3.74 (Period-5 Window)

iterated-maps · 37 views
iterated-mapsperiodic

What It Is

Logistic map inside the period-5 stability window at r=3.74 --- an island of order embedded in the chaotic regime, intermittent near its boundary

Interpretation

Standard analysis sees: left-skewed; anti-correlated (alternating); anti-persistent; blue spectrum (high-frequency power); time-irreversible (slow rise, sharp collapse); homoskedastic; monofractal; low-dimensional; stationary. The atlas additionally detects Time Reversibility:ordinal_reversal_distance. It sits beside Pell Word in the atlas (standard-bank rank 31) — a neighbor conventional features miss.

What standard analysis sees
tail heaviness0.31
asymmetry0.11
occupancy0.18
short-range corr0.04
long-range memory0.02
spectral colour0.97
periodicity0.82
complexity0.26
time-irreversibility0.08
volatility clustering0.06
multifractality0.04
dimensionality0.01
nonstationarity0.07
What the atlas adds
Time Reversibility:ordinal_reversal_distance+3.1z
time-reversal symmetry breaking via Bandt-Pompe ordinal patterns
Atlas-extreme metrics the standard bank can’t predict for this source
Julia Set:potential_variance+4.4zbank-miss 1.2σ
Julia Set:potential_smoothness+4.3zbank-miss 1.0σ
Fisher Information:velocity_spectral_gini-4.2zbank-miss 2.8σ
Klein Bottle:linear_complexity-3.9zbank-miss 1.5σ
Julia Set:escape_entropy-2.8zbank-miss 1.6σ
Boltzmann:frustration+2.5zbank-miss 2.1σ
Isochronicity:frequency_shear+2.5zbank-miss 1.9σ
Hyperbolic (Poincaré):spatio_temporal_corr+2.4zbank-miss 2.6σ

Composition

dtypefloat64
range[0.2275, 0.9349]
unique values10 / 16384
mean ± std0.632 ± 0.253

Fixed alphabet — only 10 distinct symbols across 16384 samples.

Render Gallery

Native > phase_plot
Native > phase_plotraw
Native > timeseries
Native > timeseriesraw
Native > triple_lattice
Native > triple_latticeraw
Boltzmann > lag_map
Boltzmann > lag_map
Boltzmann > spin_grid
Boltzmann > spin_grid
Cayley > default
Cayley > default
Chladni > free_plate_nodal
Chladni > free_plate_nodal
Chladni > plate_bottom
Chladni > plate_bottom
Chladni > plate_top
Chladni > plate_top
Heisenberg (Nil) (centered) > signed_log_z
Heisenberg (Nil) (centered) > signed_log_z
Heisenberg (Nil) (centered) > xy_path
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
Hodge–Laplacian > default
Inflation (Substitution) > barcode
Inflation (Substitution) > barcode
Inflation (Substitution) > d_curve
Inflation (Substitution) > d_curve
Information Theory > default
Information Theory > default
Julia Set > escape_histogram
Julia Set > escape_histogram
Klein Bottle > default
Klein Bottle > default
Laplacian > default
Laplacian > default
Logarithmic Spiral > default
Logarithmic Spiral > default
Möbius-S³ > mobius_cylinder
Möbius-S³ > mobius_cylinder
Möbius-S³ > s2_base_map
Möbius-S³ > s2_base_map
Ordinal Partition > default
Ordinal Partition > default
Penrose (Quasicrystal) > phi_spectrum
Penrose (Quasicrystal) > phi_spectrum
Persistent Homology > barcode
Persistent Homology > barcode
Persistent Homology > h1_diagram
Persistent Homology > h1_diagram
Predictability > default
Predictability > default
Recurrence Quantification > default
Recurrence Quantification > default
Spectral Analysis > default
Spectral Analysis > default
Spectral Graph > default
Spectral Graph > default
Spirograph > mode_spectrum
Spirograph > mode_spectrum
Spirograph > phasor_trajectory
Spirograph > phasor_trajectory
Symplectic > flux_grid
Symplectic > flux_grid
Symplectic > phase_space
Symplectic > phase_space
Ulam Spiral (Sacks) > default
Ulam Spiral (Sacks) > default
Ulam Spiral (Square) > default
Ulam Spiral (Square) > default
Visibility Graph > default
Visibility Graph > default
Wavelet Cascade > default
Wavelet Cascade > default

Atlas Position

Nearest neighborDistance
Tribonacci Word4.75cross-origin
Periodic Word5.05cross-origin
Pell Word5.13cross-origin

Open in Atlas →

Which Geometries Light Up

Attractor Reconstruction › Attractor Reconstruction:filling_ratiorank 302/3060.0049
AutoRegressive › AutoRegressive:ar_residual_fracrank 303/3060.0000
Bispectrum › Bispectrum:coupling_frequency_centroidrank 2/3060.7160
Catch24 › Catch24:CO_trev_1_numrank 303/306-2.8000
Catch24 › Catch24:SP_Summaries_welch_rect_area_5_1rank 303/3060.0000
Chladni › Chladni:modal_nodal_cascaderank 5/3061.9719
Chladni › Chladni:plate_low_mode_fractionrank 304/3060.0026
D4 Triality › D4 Triality:triplet_temporalrank 3/3060.8100
Heisenberg (Nil) (centered) › Heisenberg (Nil) (centered):xy_spreadrank 302/3061.0759
Hyperbolic (Poincaré) › Hyperbolic (Poincaré):spatio_temporal_corrrank 1/3060.9217
Inflation (Substitution) › Inflation (Substitution):complexity_subexponentialrank 306/3060.6166
Isochronicity › Isochronicity:frequency_shearrank 2/3060.8659
Moiré › Moiré:moire_dilation_entropyrank 303/3061.4188
Nonstationarity › Nonstationarity:vol_of_volrank 304/3060.2402
Predictability › Predictability:cond_entropy_k1rank 304/3060.0000
SL(2,ℝ) (Thurston) › SL(2,ℝ) (Thurston):cocycle_growth_burstinessrank 304/3060.0000
Symplectic › Symplectic:windowed_area_cvrank 304/3060.0000
in iterated-maps
alphabetical
← / → within domain · ⇧← / ⇧→ alphabetical · ⇧← / ⇧→ inside an open render = same view across sources

Structure Atlas — Open Atlas · GitHub