Windowsill Lab · Field Explainers · The Register

Every run,
a room of its own

The windowsill keeps receipts. Twenty-seven captured runs live here: twenty-four have rooms of their own — live explainers running each experiment's real update rules in your browser — and three, the non-equilibrium wing, run further down this very page. The register below is the shelf; start anywhere.

27captured runs
24rooms of their own
M16–M18live on this page
THE REGISTER

Every run the lab has kept receipts for

A run reproduced its target, a run returned a null or is still in flight, and a run refused its own measurement — kept because the refusal is the lesson.

The magnet ladder — statistical physics

Coherence — crowds of clocks

Arithmetic and instruments

The sky

THE NON-EQUILIBRIUM WING · LIVE ON THIS PAGE

Three experiments that never settle

Most experiments on this instrument's ladder measure systems at equilibrium. These three measure systems that never reach it: a glass that ages, a surface that roughens without limit, and activity that either spreads or goes extinct. Each panel below runs the experiment's actual dynamics, live, in your browser; the quoted numbers are from the published runs — all three green, human-reviewed.

M16

A glass that remembers its age

After a rapid quench, does a disordered magnet evolve in a way that depends on how long ago it was quenched?

Macro photograph-style painting of a dark vitreous slab in which thousands of small metallic domains are frozen mid-swirl, catching warm light.
Illustration (AI-painted) — disorder arrested mid-fall

A spin glass is a magnet with randomly competing interactions: no arrangement of its spins can satisfy every bond, so after rapid cooling it freezes into a disordered state that continues to evolve — extremely slowly — forever.

The signature is aging. Record the configuration at two different times after the quench, then measure how quickly the system decorrelates from each record. The older the system was at the time of the record, the more slowly it lets go. Below, one quenched glass and two record ages, running live.

Live · quenched ±J glass · Metropolis, T = 0.6 2-D DEMO LATTICE — INTUITION ONLY
t = 0

left · the glass (dark/light = spin) — watch domains freeze, then barely move · right · memory curves: how much the glass still matches its snapshot taken at age tw=60 (ember) vs tw=600 (moss). The old snapshot fades slower. That is aging.

0.24×scatter, age-scaled vs lag-scaled MEASURED
+0.104ΔC, old vs young at fixed lag
64disorder realizations (3-D, L=12)

The published run — a three-dimensional ±J glass, averaged over 64 disorder realizations — found that the correlation curves collapse when plotted against lag divided by age, with a residual scatter 0.24 times that of the time-translation-invariant alternative, and that at fixed lag the older system retains measurably more correlation. Time-translation invariance is broken, as aging requires.

Finite lattice, finite time, one temperature: this calibrates aging, it does not map the universal scaling function. And the demo above is a 2-D stand-in for intuition — the graded measurement is the 3-D run in the receipt.
M17

The universal roughness of growing things

When a surface grows by random local deposition, does its roughness obey a universal law?

Painted frost crystallizing along the rim of a circular window pane, the growing edge rough with self-similar bumps.
Illustration (AI-painted) — a growth front, rough at every scale

A surface growing by random arrival roughens in a constrained way: for a broad class of growth processes — the KPZ universality class — the interface width grows as time to the power 1/3, independent of microscopic details. Frost fronts, combustion fronts, and colony edges are all argued to share this exponent.

Below is the model from the published run: single-step corner growth on a ring. The interface width is plotted against time on logarithmic axes beside the theoretical slope.

Live · single-step corner growth on a ring · the lab's own model SMALL RING — THE REAL RUN USED L=4096
t = 0

left · the droplet grows, its rim wandering · right · rim roughness vs time, log-log; the guide line is slope 1/3 — the KPZ signature the run must track until this small ring saturates. Past the marked crossing the rim can't get any rougher than the ring is long, and the curve flattens away from the guide: finite size, not a failed exponent.

0.3127β measured vs exact 1/3 MEASURED
1.548z measured vs exact 3/2
0.6%random-deposition anchor error

The measurement is controlled: the same estimator was applied to two additional growth rules with exactly known, distinct exponents, and recovered both — ¼ for the Edwards–Wilkinson rule and ½ for random deposition, the latter within 0.6% of a closed-form prediction with no fitted parameters. An estimator that produced ⅓ from arbitrary data would fail both controls.

β lands 0.021 below the exact ⅓ — the documented slow approach from below, and the control (growth-without-spread) misses its own exponent in the same direction, which is how you know it's the finite window and not a defect. The height-fluctuation statistics are assigned to their class (Tracy–Widom, mirrored, as the model's negative tilt predicts), not proven as a full collapse.
M18

The knife-edge between spreading and dying

When activity can spread to neighbours or die out irreversibly, where is the threshold between survival and extinction?

Overhead view of a thin fire front advancing through sparse dry grass at night: glowing ember points in a ragged cluster, burned dark region behind, untouched grass ahead.
Illustration (AI-painted) — a spreading front, one step either side of threshold

The empty state here is absorbing: once all activity is gone, the dynamics cannot restart it. Systems with an absorbing state exhibit one of the sharpest transitions in statistical physics, with critical behaviour — the directed percolation class — conjectured to describe phenomena from the onset of turbulence to epidemic thresholds.

Below is the update rule from the published run: each cell becomes active with probability p per active neighbour (including itself). The slider crosses the measured threshold.

Live · probabilistic cellular automaton · the lab's own rule SMALL GRID — THE REAL RUN USED L=2048
p = 0.22415

left · the moss bed (ember = alive) · right · surviving fraction over time, log-log. Below the edge it crashes; above, it levels off; at the edge it slides down a power law forever. The lab's measured edge for this rule: pc = 0.22415 ± 0.00005 — the slider's home position.

[0.41, 0.55]δ bracket ∋ 0.4505 MEASURED
≠ 1.0mean-field excluded
2 GPUsindependent full runs agree

The published run reports the decay exponent as a bracket rather than a point value: one run marginally below threshold and one marginally above, verified to curve in opposite directions, bound the exponent between them. The bracket contains the accepted directed-percolation value (0.4505) and excludes the mean-field value (1.0). An independent full run on different hardware reproduced the result.

A bounded consistency check, not a precision measurement: one lattice size, no finite-size collapse claimed, and the exponent is bracketed, never pinned. Three controls ran alongside — far-below dies visibly differently, far-above levels off, and from a truly empty grid nothing ever switches on.