Collatz Stopping Times
number-theory · 37 views
number-theoryarithmetic
What It Is
Collatz total stopping times --- how many map steps (counting both the n/2 halvings and the 3n+1 steps) each integer takes to reach 1. Wildly erratic, with typical values around 7·log₂(n) (asymptotic mean 3·ln(n)/ln(4/3) ≈ 7.23·log₂(n); fitted slope ≈ 7.0 over n in [1e4, 5e5]) but enormous outliers
Interpretation
Standard analysis sees: multifractal. The atlas detects no named structure beyond this. It sits beside Surface Wind (ORD 5-min) in the atlas (standard-bank rank 46) — a neighbor conventional features miss.
What standard analysis sees
tail heaviness0.58
asymmetry0.75
occupancy0.24
short-range corr0.49
long-range memory0.60
spectral colour0.49
periodicity0.39
complexity0.46
time-irreversibility0.21
volatility clustering0.52
multifractality0.86
dimensionality0.75
nonstationarity0.59
What the atlas adds
Nothing beyond the standard reading — this source’s structure is already captured by standard features; the atlas adds no named residual.
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 > free_plate_nodal
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) | 4.17 | cross-origin |
| Earthquake Magnitudes | 4.29 | cross-origin |
| Poisson Counts | 4.31 | cross-origin |
Which Geometries Light Up
Navier-Stokes › Navier-Stokes:ess_rescaling_gain | rank 306/306 | -0.2047 |
Septagonal (Danzer) › Septagonal (Danzer):z_conjugate | rank 302/306 | -0.6062 |
Visibility Graph › Visibility Graph:degree_r_squared | rank 5/306 | 0.9600 |
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