Collatz Stopping Times

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: no strongly notable standard properties. The atlas finds no named structure, but the source is distinctively extreme on Spirograph:gear_rationality (-3.1z) — beyond what the standard bank predicts for it. It sits beside Surface Wind (ORD 5-min) in the atlas (standard-bank rank 60) — a neighbor conventional features miss.

Composition

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

Heisenberg (Nil) (centered) > signed_log_z

Heisenberg (Nil) (centered) > xy_path

Hodge–Laplacian > default

Inflation (Substitution) > barcode

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

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

Ulam Spiral (Sacks) > default

Ulam Spiral (Square) > default

Visibility Graph > default

Wavelet Cascade > default

Atlas Position

Open in Atlas →

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