OBSERVATION CHAMBER / ACTIVE
Block-spin coarse-grain a 2D Ising-like lattice and observe magnetization, correlations, and effective-coupling flow across scale.
ROUTE 72 / GROWTH / SCALE FLOW
BLOCK-SPIN / METROPOLIS
Coarse-grain the same periodic lattice with R₂ majority blocks. Read magnetization, correlation, and an effective-coupling proxy as the field flows toward an ordered, disordered, or critical basin.
Canvas 2D is unavailable. The scale ladder and numerical readings remain available.
The large field is the selected scale. The lower ladder shows 1×→64× block-spin images; the flow map compares |m|, C1, and fixed-point proximity.
All calculations stay local in this browser.
SCALE READOUT
C1 and C2 use periodic horizontal and vertical pairs. G1 subtracts the disconnected magnetization background; Keff is intentionally labelled a proxy.
| SCALE | SIDE | m | C1 | C2 | G1 | Keff | FLOW d | PFP |
|---|
DETERMINISTIC SELF-TEST
CRITICAL / PASS
| CHECK | VALUE | LIMIT | RESULT |
|---|
OBSERVATION CONTRACT
The primary object is a 64×64 spin field and its R₂ block-spin ladder. Metropolis samples the local Ising-like energy at fixed K; coarse graining maps four parent spins to one child. The numeric path across scale is the observation.
WHAT TO WATCH
MODEL NOTE
H = −JΣ⟨ij⟩sᵢsⱼ, p(flip)=min(1,e⁻ᴷΔE), R₂: {s₁,s₂,s₃,s₄}→sign majority
The 2D reference is Kc = ½ ln(1+√2), Tc/J = 1/Kc. Keff and fixed-point proximity are bounded browser proxies.
PLAY caps at 12 sweeps/s; each sweep attempts 4096 sites and redraws only after state changes.
m = N⁻¹Σᵢsᵢ, C₁ = (2N)⁻¹Σᵢ(sᵢsᵢ₊ₓ+sᵢsᵢ₊ᵧ), C₂ uses distance two, G₁ = C₁−m², and Keff = atanh(clamp(C₁,−0.999999,0.999999)). The flow distance is a finite normalized Euclidean distance between adjacent metric rows.
OBSERVATION GUIDE
Start at CRITICAL and compare the large field with the seven-card R₂ ladder. Then press STEP and read how the same observables move with scale.
This is a finite Ising-like numerical model, not a full Monte Carlo sampler, an exact RG calculation, or a physical temperature measurement.
Runs inside the browser with no upload and no registration.
This chamber runs a deterministic 64×64 Ising-like lattice in your browser. Metropolis updates, block-spin coarse graining, calculations, reports, and images stay local. It does not measure visitors, devices, or physical matter.
This chamber belongs to Growth & Thresholds.
GROWTH Back to Growth & Thresholds Route.