Collatz Flights
number_theory · 36 views
number_theory
What It Is
Peak altitude of Collatz orbits --- how high consecutive integers fly before crashing to 1
Interpretation
Standard analysis sees: right-skewed; time-irreversible (slow rise, sharp collapse). The atlas finds no named structure, but the source is distinctively extreme on Boltzmann:dominant_lag (+4.0z) — beyond what the standard bank predicts for it.
What standard analysis sees
tail heaviness0.82
asymmetry0.88
occupancy0.30
short-range corr0.17
long-range memory0.34
spectral colour0.52
periodicity0.75
complexity0.51
time-irreversibility0.08
volatility clustering0.44
multifractality0.44
dimensionality0.63
nonstationarity0.46
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
Boltzmann:dominant_lag | +4.0z | bank-miss 1.7σ |
Attractor Reconstruction:lyap_sum | -4.0z | bank-miss 2.4σ |
Composition
dtypefloat64
range[13.65, 23.93]
unique values14456 / 16384
mean ± std15 ± 1.13
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/Collatz_Flights.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Collatz_Flights.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Collatz_Flights.png)
Inflation (Substitution) > barcode
/d_curve/Collatz_Flights.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/Collatz_Flights.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/Collatz_Flights.png)
Ulam Spiral (Sacks) > default
/default/Collatz_Flights.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Aliquot Orbit Lengths | 4.20 | |
| Divisor Count | 4.29 | |
| Linux ELF x86-64 | 4.94 | cross-domain |
Which Geometries Light Up
Boltzmann › Boltzmann:dominant_lag | rank 1/298 | 1024.0000 |
Spectral Analysis › Spectral Analysis:spectral_bandwidth | rank 5/298 | 0.1721 |
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