Universe Timeline
A live simulation of the substrate's life-cycle. Cosmogenesis (substrate iterates from L=1 to L=3), habitable epoch (matter modes ring stably while local carve releases waves), then dilution death (capacity degrades, bound modes lose support, regions go void). Master-clock constants tick in real time. Carve events flash where local matter exceeds local capacity. The death frame is partly extrapolation — see notes below.
Substrate state
Master clock
Timeline (τ)
What you're looking at — read this
Substrate. A 2D Sierpinski carpet, the planar analog of the 3D Menger sponge. Each iteration replaces every surviving cell with 8 sub-cells, dropping the central one — same carve rule, lower dimension, easier to render. The 3D version follows the same dynamics with the 20/27 ratio instead of 8/9.
Cosmogenesis (τ ∈ [0, 0.30]). The substrate iterates. L grows continuously from
1 to 3 — at integer L's the cell count snaps to 8, 64, 512. Between integers we interpolate
cell visibility. Void fraction grows toward its limit, surface-to-volume ratio diverges, mode
count grows. Master-clock formula 1/α(L) = Sb³ + P + (Pb)²·(P/k)^L is computed live.
Habitable epoch (τ ∈ [0.30, 0.70]). L holds at 3. The matter density field
ρ(c, t) lives on each cell. ρ rings according to the cell's local mode structure (real
eigenmodes from
experiments/ringer/eigendata_L3.json). The dynamic-carve equation
∂ρ/∂t = -η·‖ρ - ρ_cap‖²·ρ + J runs continuously: where local matter occupation
exceeds local capacity (ρ > ρ_cap), the cell flashes (carve event — wave/heat release) and
ρ relaxes back toward ρ_cap. Capacity is bipartite: degree-3 corner cells host less than
degree-4 edge cells.
Dilution death (τ ∈ [0.70, 1.00]). ρ_cap globally degrades, simulating substrate dilution at L→∞ where surface→∞ but mode-supporting volume→0. Once a cell's capacity falls below its current occupation, the carve runs continuously and ρ drains to zero. Cells go permanently dark. End state: void.
What's measured vs extrapolated. The cell positions, eigenmodes, master-clock formula, and carve nonlinearity are all framework-grounded with on-disk receipts. The "dilution death" frame is qualitative — it visualizes the L→∞ limit of the carve dynamics, but the exact rate of capacity degradation is a dial, not a measured quantity. Treat the death as cartoon; treat the cosmogenesis and habitable ringing as live.
Sources: Triune Necessity, Research Log, the Dynamic Carve Hypothesis (paper repo), the L3 ringer eigendata, the master-clock residual fit (β = 1.010 ± 0.094, ρ_geomean = 0.092 vs predicted 0.10).