Predictions, written before any model was trained

A Rule 30 cellular automaton forms a dark triangular history crossed by an orange horizontal horizon.

The claim under test

Planned setup

Measurements

Predictions

What would count against the claim

Limits known in advance

Added after the Rule 30 pilot, before the ladder reached Rules 170 and 90

The claim under test

The more a visual phenomenon behaves like a complex, noise-like system in the real world, the worse a noise model (a diffusion model) does at keeping it coherent.

Rule 30 stands in for smoke. Its ground truth is exact and cheap, and a single wrong cell can be located. The spacetime picture of a one-dimensional automaton is a video of a one-dimensional world: row 0 is the first frame and time runs down the image. Conditioning a model on row 0 and asking for the rest is image-to-video.

The claim bundles two properties, and the rule ladder is chosen to separate them:

Rule	Class	Single row looks like	A one-cell defect	Chosen to test
4	2	sparse dots	stays one cell or vanishes	the easy floor
184	2	traffic of particles	moves, bounded	conserved motion
170	2	fair-coin noise	rides one diagonal, never grows	noise-like pictures without sensitivity
110	4	structured noise	spreads irregularly	complex, universal
90	3	fair-coin noise	spreads at speed 1	sensitivity with a closed form (Lucas' theorem)
30	3	fair-coin noise	spreads, one side at speed 1	the irreducible exemplar

Rule 170 separates looking like noise from amplifying error. Rule 90 separates amplifying error from having no shortcut.

Measurements

Symbol	Meaning	Lawful / perfect value
v	fraction of cells in rows 1..39 that differ from the rule applied to their actual parents	0
v(t)	the same, row by row	0
TV	total variation distance between the 3×3 window distributions of samples and of exact evolutions	0
acc(t)	fraction of row t equal to the exact evolution from the same row 0	1 (1/2 means no information)
H	first row where acc(t) < 0.75	none within 39 rows
noisy runner	the exact rule plus independent flips at the painter's own per-row v(t)	—

Predictions

ID	Prediction	Confidence	Fails if
P1	The painter learns the look: for every rule, the TV of its unconditional samples is under one fifth of the TV of fair-coin noise	75%	any rule at or above one fifth
P2	Lawfulness tracks dynamics more than appearance: v(170) < v(30) and v(170) < v(110)	70%	either inequality reversed
P3	Coherence tracks sensitivity: H for rules 4, 184 and 170 each exceeds H for rules 30, 90 and 110, and rules 4 and 184 show no horizon within 39 rows	70%	any low-sensitivity rule loses coherence before any high-sensitivity rule
P4	Rule 30 is short-lived: H(30) ≤ 20 rows with 256 sampling steps	65%	H(30) > 20 or no horizon
P5	Mechanism: the noisy runner driven by the painter's per-row v(t) predicts the painter's acc(t) within 0.1 at every row, for rules 30, 90 and 110	50%	a gap above 0.1 at any row for any of the three
P6	The shortcut does not help the painter: \|H(90) − H(30)\| ≤ 0.3 · H(30)	50%	Rule 90 differs by more than 30%
P7	Sequential compute helps only a little: going from 32 to 512 sampling steps raises H(30) by less than a factor of 2	60%	H(30) at least doubles
P8	The runner is exact: v = 0 and acc(t) = 1 on every row for all six rules	95%	any violation

Added after the Rule 30 pilot, before the ladder reached Rules 170 and 90

Written on 28 September 2026, while the ladder was training Rule 4. The pilot's per-neighbourhood errors: Rule 30 is l ⊕ (c ∨ r). Where the centre is 1 the output is ¬l, a single-cell dependency, and the painter errs in 0.4–1.6% of those cases. Where the centre is 0 the output is l ⊕ r, a parity of two cells, and it errs in 2.6–4.5% of them. If parity is what the painter finds hard, rules made only of parity or only of copying should sit on either side of Rule 30.

ID	Prediction	Confidence	Fails if
P9	v(90) > v(30) > v(170), for unconditional samples and for samples from the true row 0. Rule 90 is l ⊕ r in every case; Rule 170 copies one cell.	70%	either inequality reversed in either setting

Predictions, written before any model was trained?

The claim under test?

Planned setup?

Measurements?

Predictions?

What would count against the claim?

Limits known in advance?

Added after the Rule 30 pilot, before the ladder reached Rules 170 and 90?

Predictions, written before any model was trained

The claim under test

Planned setup

Measurements

Predictions

What would count against the claim

Limits known in advance

Added after the Rule 30 pilot, before the ladder reached Rules 170 and 90