3D Equation Automata
3D Moore Lattice · WebGL Instanced Architecture · Periodic Boundaries
p = —
step 0
Slice View: All
Lattice & Parameters
Grid Size (L)
32³ (Recommended, Faster)
40³ (Balanced)
48³ (Dense / High-End)
Initial Probability p₀
6 / 27 ≈ 0.22222 [3D Critical Limit]
1 / 3 ≈ 0.33333 [Antiferromagnetic Point]
2 / 3 ≈ 0.66667 [Ferromagnetic Point]
cos²(π/8) ≈ 0.85355 [2D Parameter]
Von Neumann threshold (h)
h ≥ 1
h ≥ 2
h ≥ 3 [3D Correct Scaling]
h ≥ 4
Moore threshold (g)
g ≤ 12
g ≤ 16
g ≤ 18 [3D Critical Limit]
g ≤ 20
PAUSE
RESET
Live Statistics
Step
0
Alive (count₁)
—
Alive fraction
—
3D Vector output
—
Phase
—
3D Geometrical Scale
Max Moore
26 Neighbors
Full Element Cube
27 Cells
Direction Plane
3 × 3 = 9 Cells
Coupling:
g/27 > (1−p)·p
Target Density:
6/27 ≈ 0.22222
Quadratic Bridge:
p² − p + 6/27 = 0
Exact 3D Roots:
1/3
,
2/3