O-R Lattice: Collatz Sequence Visualizer
Explore 3x+1 sequences through the (o,r) coordinate system
Starting value (x₀):
Plot Sequence
Clear
Examples:
27
31
63
127
70055
77031
Show even terms on lattice
Layers:
Grid
Axes
Path
OE Blocks
λₘ-layer
λₓ-layer
ε-layer
Animate to λₓ
O step (3x+1)/2: moves (o,r) → (o-1, r-1)
E step x/2^β (divide out all 2s): moves (o,r) → (o, r+β-2)
Colored boxes: ((OE)+E+) blocks accelerate multiple O steps
Starting Value (x₀)
Sequence (OE notation):
-
Sequence length:
-
((OE)+E+) blocks:
-
Heatmap: (α, β) Distribution
For odd x: α = v₂(x+1), β = v₂(3x+1)