Equation Automata

2D Ising Projection · Toroidal Boundary · tan²(x) + tan(x) emergence

p = —
step 0
Initial Probability
Live Statistics
Step 0
Alive (count₁)
Alive fraction
tan²+tan output
Kc reference 0.44069
Phase
Key Identities
tan(π/8) √2 − 1
tanh(Kc) √2 − 1
gd(2Kc) π/4
s = tan(π/8) tanh(Kc)
Coupling: g/8 > (1−p)·p Quadratic: p² − p + 1/8 = 0 Roots: cos²(π/8) , sin²(π/8) Projection: tan(π/8) = tanh(Kc)