OBSERVATION CHAMBER / ACTIVE
Observe heat diffusion on a weighted graph through Laplacian eigenmodes, spectral gap, heat trace, and community mixing.
ROUTE 69 / STRUCTURE / GRAPH DIFFUSION
LAPLACIAN / HEAT EQUATION
Read the same weighted graph as topology, spectrum, and heat flow. The canvas shows values on vertices; the readouts keep the numerical contract in view.
Canvas 2D is unavailable. The deterministic graph and numerical readings remain available.
Each vertex stores u. Edge brightness follows |uᵢ − uⱼ|; the lower bars show λ in ascending order. Select a vertex with pointer or touch.
All calculations stay local in this browser.
SPECTRAL READOUT
For bridge OFF, λ₁≈0 and the zero multiplicity is two. Bridge ON makes the graph connected, so λ₁ becomes positive.
DETERMINISTIC SELF-TEST
BRIDGE OFF / PASS
| CHECK | VALUE | LIMIT | RESULT |
|---|
OBSERVATION CONTRACT
The field is a scalar value on vertices. L = D − A is built from the weighted adjacency matrix, and u(t) = exp(−tL)u₀ is evaluated in the symmetric eigenbasis. No walkers, membrane vibration, clock synchronization, or network animation is used.
WHAT TO WATCH
MODEL NOTE
L = D − A, L1 = 0, Lvₖ = λₖvₖ
The graph has at most 24 vertices. The solver is a deterministic Jacobi decomposition with residual and orthogonality checks.
du/dt = −Lu and u(t) = Σₖ e⁻ᵗλₖ (vₖᵀu₀)vₖ. The heat trace is Tr(e⁻ᵗᴸ) = Σₖe⁻ᵗλₖ; the Dirichlet energy is uᵀLu = Σ_(i,j) wᵢⱼ(uᵢ−uⱼ)².
OBSERVATION GUIDE
Start with TWO COMMUNITIES and BRIDGE OFF. Select FIELD, then STEP. The contrast signal fades inside each component while the zero modes stay visible.
This is a finite weighted-graph heat model, not a particle simulation, a physical heat measurement, or a full-scale network solver.
Runs inside the browser with no upload and no registration.
This chamber runs a deterministic weighted-graph heat model in your browser. The graph, calculations, reports, and images stay local. It does not measure visitors, devices, social networks, or physical heat.
This chamber belongs to Structures & Symmetries.
STRUCTURE Back to Structures & Symmetries Route.