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λ — Lyapunov Exponent
Trajectory
Modulus Sweep
Starting value n₀ (odd)
Iterations N
N
5000
Modulus level M (mod 2^M)
M
10
Averages log|T′| over all 2^(M−1) odd residues mod 2^M for each level 2…M.
▶ Compute λ
λ estimate
—
avg halvings v̄₂
—
log(3/4)
−0.287682
|Δ from ref|
—
T(n)
= (3n+1) / 2^v₂(3n+1)
|T′(n)|
= 3 / 2^v₂(3n+1)
λ
= log 3 − v̄₂ · log 2
heuristic: λ ≈
log(3/4)
≈ −0.2877
Other Sims
→ StormManifold
→ AXLE Operator Mode
Convergence
Halvings Histogram
Orbit Trace