Logistic r=3.2 (Period-2)

iterated-maps · 37 views
iterated-mapsperiodic

What It Is

Logistic map in stable period-2 --- output alternates between two fixed values, the simplest oscillation after the first bifurcation

Interpretation

Standard analysis sees: bounded / light-tailed; few distinct values; anti-correlated (alternating); anti-persistent; strongly periodic; low-complexity (predictable, not noise-like); homoskedastic; monofractal; stationary. The atlas finds no named structure, but the source is distinctively extreme on Nonstationarity:change_quantiles_mid (+7.8z) — beyond what the standard bank predicts for it.

What standard analysis sees
tail heaviness0.00
asymmetry0.41
occupancy0.08
short-range corr0.00
long-range memory0.00
spectral colour0.27
periodicity1.00
complexity0.03
time-irreversibility0.57
volatility clustering0.03
multifractality0.00
dimensionality0.34
nonstationarity0.00
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
Nonstationarity:change_quantiles_mid+7.8zbank-miss 1.8σ
Heisenberg (Nil) (centered):xy_spread+5.7zbank-miss 2.2σ
Klein Bottle:linear_complexity-3.9zbank-miss 1.5σ
Möbius-S³:hopf_fiber_coherence-3.5zbank-miss 2.8σ
Mostow Rigidity:margulis_ratio+3.4zbank-miss 1.3σ
Julia Set:escape_entropy-3.2zbank-miss 1.0σ
Visibility Graph:assortativity-3.1zbank-miss 1.6σ
Nonstationarity:metric_volatility-2.9zbank-miss 2.5σ

Composition

dtypefloat64
range[0.513, 0.7995]
unique values2 / 16384
mean ± std0.656 ± 0.143

Binary sequence — two distinct symbols.

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
Logistic r=3.5 (Period-4)4.57
Sine Map (Feigenbaum)6.03
Logistic Edge-of-Chaos6.08

Open in Atlas →

Which Geometries Light Up

2-adic › 2-adic:multiscale_markov_predictabilityrank 1/3061.0000
2-adic › 2-adic:valuation_spectral_concentrationrank 1/3061.0000
2-adic › 2-adic:valuation_transition_predictabilityrank 2/3061.0000
Attractor Reconstruction › Attractor Reconstruction:filling_ratiorank 306/3060.0020
AutoRegressive › AutoRegressive:ar_residual_fracrank 305/3060.0000
Cantor Set › Cantor Set:bit_plane_autocorrelationrank 1/3061.0000
Catch24 › Catch24:DN_Spread_Stdrank 1/3060.5000
Catch24 › Catch24:FC_LocalSimple_mean3_stderrrank 2/3061.3333
Catch24 › Catch24:CO_Embed2_Dist_tau_d_expfit_meandiffrank 305/3060.0000
Catch24 › Catch24:CO_f1ecacrank 306/3060.3161
Catch24 › Catch24:SP_Summaries_welch_rect_area_5_1rank 306/3060.0000
Cayley › Cayley:delta_hyp_normrank 306/3060.0000
Chladni › Chladni:plate_low_mode_fractionrank 306/3060.0000
D4 Triality › D4 Triality:gram_consistencyrank 305/3060.0000
E8 Lattice › E8 Lattice:std_profilerank 305/3060.0000
Heisenberg (Nil) (centered) › Heisenberg (Nil) (centered):area_length_ratiorank 1/3060.4054
Heisenberg (Nil) (centered) › Heisenberg (Nil) (centered):xy_spreadrank 1/3064729.7977
Higher-Order Statistics › Higher-Order Statistics:c3_energyrank 304/3060.0000
Higher-Order Statistics › Higher-Order Statistics:bicoherence_maxrank 305/3060.0000
Higher-Order Statistics › Higher-Order Statistics:kurt_maxrank 305/3060.0000
Higher-Order Statistics › Higher-Order Statistics:skew_meanrank 306/3060.0000
Hodge–Laplacian › Hodge–Laplacian:source_fractionrank 306/3060.0156
Hyperbolic (Poincaré) › Hyperbolic (Poincaré):curvature_structurerank 305/3061.0000
Hyperbolic (Poincaré) › Hyperbolic (Poincaré):temporal_variancerank 306/3060.0000
H² × ℝ (Thurston) › H² × ℝ (Thurston):hyperbolic_step_dispersionrank 1/3069.4349
H² × ℝ (Thurston) › H² × ℝ (Thurston):hyperbolic_triangle_arearank 304/3060.0000
Information Theory › Information Theory:compression_ratiorank 306/3060.0022
Julia Set › Julia Set:potential_smoothnessrank 1/3067045.5463
Julia Set › Julia Set:potential_variancerank 1/30646408596.8745
Julia Set › Julia Set:escape_entropyrank 305/3062.5671
Klein Bottle › Klein Bottle:wht_spectral_kurtosisrank 1/3069.7041
Klein Bottle › Klein Bottle:linear_complexityrank 304/3060.0078
Laplacian › Laplacian:biharmonic_ratiorank 1/30615.9980
Moiré › Moiré:moire_max_coherencerank 1/3061.0000
Moiré › Moiré:moire_integer_excessrank 4/3060.5434
Moiré › Moiré:moire_dilation_entropyrank 306/3060.9496
Mostow Rigidity › Mostow Rigidity:margulis_ratiorank 1/3061.0000
Multi-Scale Wasserstein › Multi-Scale Wasserstein:w_stdrank 305/3060.0000
Multi-Scale Wasserstein › Multi-Scale Wasserstein:w_finerank 306/3060.0000
Multi-Scale Wasserstein › Multi-Scale Wasserstein:w_meanrank 306/3060.0000
Möbius-S³ › Möbius-S³:hopf_fiber_coherencerank 306/3060.0000
Navier-Stokes › Navier-Stokes:ess_rescaling_gainrank 304/3060.0000
Nonstationarity › Nonstationarity:change_quantiles_midrank 1/3061.0000
Nonstationarity › Nonstationarity:dynamic_couplingrank 306/3060.0000
Nonstationarity › Nonstationarity:metric_volatilityrank 306/3060.0000
Nonstationarity › Nonstationarity:trajectory_dimrank 306/3060.0000
Nonstationarity › Nonstationarity:vol_of_volrank 306/3060.0000
Predictability › Predictability:cond_entropy_k1rank 305/3060.0000
Projective ℙ² › Projective ℙ²:distance_stdrank 1/3060.3073
SL(2,ℝ) (Thurston) › SL(2,ℝ) (Thurston):cocycle_growth_burstinessrank 306/3060.0000
SL(2,ℝ) (Thurston) › SL(2,ℝ) (Thurston):cocycle_growth_raterank 306/3060.0000
Sol (Thurston) › Sol (Thurston):integrated_walk_smoothnessrank 304/306-0.2000
Sol (Thurston) › Sol (Thurston):path_lengthrank 305/3066350.4459
Spectral Analysis › Spectral Analysis:spectral_peakednessrank 1/3060.9998
Spectral Analysis › Spectral Analysis:spectral_r2rank 305/3060.0000
Spectral Analysis › Spectral Analysis:spectral_bandwidthrank 306/3060.0000
Spherical S² › Spherical S²:concentrationrank 1/3061.0000
Spherical S² › Spherical S²:hemisphere_balancerank 303/3060.0000
Spherical S² › Spherical S²:angular_spreadrank 306/3060.0000
Symplectic › Symplectic:windowed_area_cvrank 305/3060.0000
Symplectic › Symplectic:phase_volume_exploredrank 306/3060.0020
S² × ℝ (Thurston) › S² × ℝ (Thurston):great_circle_dispersionrank 1/3063.1416
S² × ℝ (Thurston) › S² × ℝ (Thurston):sphere_concentrationrank 306/3060.0002
Time Reversibility › Time Reversibility:increment_skewness_maxrank 302/3060.0005
Visibility Graph › Visibility Graph:assortativityrank 306/306-0.4966
Wavelet Cascade › Wavelet Cascade:scale_gini_dispersionrank 306/3060.0000
Zariski › Zariski:residual_sloperank 1/306-0.0406
Zipf–Mandelbrot (16-bit) › Zipf–Mandelbrot (16-bit):gini_coefficientrank 305/3060.0000
Zipf–Mandelbrot (8-bit) › Zipf–Mandelbrot (8-bit):gini_coefficientrank 305/3060.0000
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