Collatz Stopping Times
number_theory · 36 views
number_theory
What It Is
Collatz stopping times --- how many steps each integer takes to reach 1. Wildly erratic, with typical values around 3.5·log₂(n) but enormous outliers
Interpretation
Standard analysis sees: no strongly notable standard properties. The atlas finds no named structure, but the source is distinctively extreme on Spirograph:gear_rationality (-3.3z) — beyond what the standard bank predicts for it. It sits beside Surface Wind (ORD 5-min) in the atlas (standard-bank rank 55) — a neighbor conventional features miss.
What standard analysis sees
tail heaviness0.62
asymmetry0.78
occupancy0.22
short-range corr0.48
long-range memory0.58
spectral colour0.49
periodicity0.35
complexity0.45
time-irreversibility0.26
volatility clustering0.49
multifractality0.54
dimensionality0.75
nonstationarity0.60
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
Spirograph:gear_rationality | -3.3z | bank-miss 1.1σ |
Persistent Homology:n_significant_features | +2.4z | bank-miss 1.7σ |
Composition
dtypefloat64
range[24, 399]
unique values45 / 16384
mean ± std134 ± 56.6
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_Stopping_Times.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Collatz_Stopping_Times.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Collatz_Stopping_Times.png)
Inflation (Substitution) > barcode
/d_curve/Collatz_Stopping_Times.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_Stopping_Times.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_Stopping_Times.png)
Ulam Spiral (Sacks) > default
/default/Collatz_Stopping_Times.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Surface Wind (ORD 5-min) | 4.46 | cross-domain |
| Earthquake Magnitudes | 4.48 | cross-domain |
| Poisson Counts | 4.50 | cross-domain |
Which Geometries Light Up
Navier-Stokes › Navier-Stokes:ess_quality | rank 298/298 | -0.2047 |
Persistent Homology › Persistent Homology:total_persistence | rank 4/298 | 5.6472 |
Persistent Homology › Persistent Homology:n_significant_features | rank 5/298 | 19.9000 |
Septagonal (Danzer) › Septagonal (Danzer):z_conjugate | rank 296/298 | -0.6062 |
Visibility Graph › Visibility Graph:degree_r_squared | rank 5/298 | 0.9600 |
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