Baker Kick Trajectory
Collatz on the (Z/NZ)² torus
Starting number n
Torus scale N
9
27
81
Play
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Step
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Speed:
5
steps/sec
Foliation line (a = log₂3 × b)
Kick vectors
Cell error gauge
Danger zone glow
Trajectory trail
Cell Error (cumulative)
0.000
Deficit = ν₃ − t/3
0.000
Position (ν₂ mod N, ν₃ mod N)
(0, 0)
Baker's theorem:
|a − log₂3·b| > C/max(|a|,|b|)
κ
Dangerous cells cluster near the foliation line but can never sit exactly on it.
Baker Kick:
During a v₂=1 run of d steps, cell error shifts by d×(1−log₂3) ≈ −0.585d.
The trajectory is pushed
away
from the dangerous region.
Green
= safe steps,
Red glow
= dangerous zone,
Arrow
= kick direction.
t=0 | ν₂=0 ν₃=0